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Submitted Preprints 
M. Fornasier, T. Klock, M. Rauchensteiner Robust and resource efficient identification of two hidden layer neural networks, July 2019.
[Abstract] [BibTeX]

Abstract We address the structure identification and the uniform approximation of two fully nonlin ear layer neural networks of the type f(x) = 1T h(BT g(AT x)) on Rd, where g = (g1, . . . , gm0 ), h = (h1,...,hm1), A = (a1...am0) ∈ Rd×m0 and B = (b1...bm1) ∈ Rm0×m1, from a small number of query samples. The solution of the case of two hidden layers presented in this paper is crucial as it can be further generalized to deeper neural networks. We approach the problem by sampling actively finite difference approximations to Hessians of the network. Gathering several approximate Hessians allows reliably to approximate the matrix subspace W spanned by symmetric tensors a1 ⊗ a1 , . . . , am0 ⊗ am0 formed by weights of the first layer together with theentangledsymmetrictensorsv1⊗v1,...,vm1 ⊗vm1,formedbysuitablecombinationsof the weights of the first and second layer as vl = AG0bl/∥AG0bl∥2, l ∈ [m1], for a diagonal matrix G0 depending on the activation functions of the first layer. The identification of the 1rank symmetric tensors within W is then performed by the solution of a robust nonlinear program, maximizing the spectral norm of the competitors constrained over the unit Frobe nius sphere. We provide guarantees of stable recovery under a posteriori verifiable conditions. Once the 1rank symmetric tensors {ai ⊗ ai, i ∈ [m0]} ∪ {vl ⊗ vl, l ∈ [m1]} are computed, we address their correct attribution to the first or second layer (ai’s are attributed to the first layer). The attribution to the layers is currently based on a semiheuristic reasoning, but it shows clear potential of reliable execution. Having the correct attribution of the ai,vl to the respective layers and the consequent deparametrization of the network, by using a suit ably adapted gradient descent iteration, it is possible to estimate, up to intrinsic symmetries, the shifts of the activations functions of the first layer and compute exactly the matrix G0. Eventually, from the vectors vl = AG0bl/∥AG0bl∥2’s and ai’s one can disentangle the weights bl’s, by simple algebraic manipulations. Our method of identification of the weights of the network is fully constructive, with quantifiable sample complexity, and therefore contributes to dwindle the blackbox nature of the network training phase. We corroborate our theoretical results by extensive numerical experiments, which confirm the effectiveness and feasibility of the proposed algorithmic pipeline. 
BibTeX:
@unpublished{FKR2019,
author = {Fornasier, Massimo and Klock, Timo and Rauchensteiner, Michael},
title = {Robust and resource efficient identification of two hidden layer neural networks},
year = {2019},
doi = {https://arxiv.org/abs/1907.00485}
}

P. van Meurs and M. Morandotti Discretetocontinuum limits of particles with an annihilation rule, July 2018.
[Abstract] [BibTeX]

Abstract In the recent trend of extending discretetocontinuum limit passages for gradient flows of singlespecies particle systems with singular and nonlocal interactions to particles of opposite sign, any annihilation effect of particles with opposite sign has been sidestepped. We present the first rigorous discretetocontinuum limit passage which includes annihilation. This result paves the way to applications such as vortices, charged particles, and dislocations. In more detail, the discrete setting of our discretetocontinuum limit passage is given by particles on the real line. Particles of the same type interact by a singular interaction kernel, those of opposite sign interact by a regular one. If two particles of opposite sign collide, they annihilate, i.e., they are taken out of the system. The challenge for proving a discretetocontinuum limit is that annihilation is an intrinsically discrete effect where particles vanish instantaneously in time, while on the continuum scale the mass of the particle density decays continuously in time. The proof contains two novelties: (i) the empirical measures of the discrete dynamics (with annihilation rule) satisfy the continuum evolution equation that only implicitly encodes annihilation, and (ii) by imposing a relatively mild separation assumption on the initial data we can identify the limiting particle density as a solution to the same continuum evolution equation. 
BibTeX:
@unpublished{vMM2018,
author = {Patrick van Meurs, and Marco Morandotti},
title = {Discretetocontinuum limits of particles with an annihilation rule},
year = {2018},
doi = {https://arxiv.org/abs/1807.11199}
}

I. Lucardesi, M. Morandotti, R. Scala, and D. Zucco. Confinement of dislocations inside a crystal with a prescribed external strain, July 2018.
[Abstract] [BibTeX]

Abstract A system of n screw dislocations in an isotropic crystal undergoing antiplane shear is studied in the framework of linear elasticity. Imposing a suitable boundary condition for the strain, namely requesting the nonvanishing of its boundary integral, results in a confinement effect. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The result is obtained by formulating the problem via the core radius approach and by studying the asymptotics as the core size vanishes. An iterative scheme is devised to prove the main result. This work sets the basis for studying the upscaling problem, i.e., the limit as n tends to infity, which is treated in [17]. 
BibTeX:
@unpublished{LMSZ2018,
author = {Ilaria Lucardesi, Marco Morandotti, Riccardo Scala, and Davide Zucco},
title = {Confinement of dislocations inside a crystal with a prescribed external strain},
year = {2018},
doi = {https://arxiv.org/abs/1610.06852}
}

M. Iwen, F. Krahmer, S. KrauseSolberg and J.Maly. On Recovery Guarantees for OneBit Compressed Sensing on Manifolds, July 2018.
[Abstract] [BibTeX]

Abstract This paper studies the problem of recovering a signal from onebit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension. We provide a convex recovery method based on the Geometric MultiResolution Analysis and prove recovery guarantees with a nearoptimal scaling in the intrinsic manifold dimension. Our method is the first tractable algorithm with such guarantees for this setting. The results are complemented by numerical experiments confirming the validity of our approach. 
BibTeX:
@unpublished{IwenKrahmerKrauseSolbergMaly18,
author = {Mark A. Iwen, Felix Krahmer, Sara KrauseSolberg, Johannes Maly},
title = {On Recovery Guarantees for OneBit Compressed Sensing on Manifolds},
year = {2018},
doi = {https://arxiv.org/abs/1807.06490}
}

F. Krahmer, C. Kümmerle and H. Rauhut. A Quotient Property for Matrices with HeavyTailed Entries and its Application to NoiseBlind Compressed Sensing, June 2018.
[Abstract] [BibTeX]

Abstract For a large class of random matrices A with i.i.d. entries we show that the $\ell_1$quotient property holds with probability exponentially close to 1. In contrast to previous results, our analysis does not require concentration of the entrywise distributions. We provide a unified proof that recovers corresponding previous re sults for (sub)Gaussian and Weibull distributions. Our findings generalize known results on the geometry of random polytopes, providing lower bounds on the size of the largest Euclidean ball contained in the centrally symmetric polytope spanned by the columns of A. At the same time, our results establish robustness of noiseblind l1decoders for recovering sparse vectors x from underdetermined, noisy linear measurements y=Ax+w under the weakest possible assumptions on the entrywise distributions that allow for recovery with optimal sample complexity even in the noiseless case. Our analysis predicts superior robustness behavior for measurement matrices with superGaussian entries, which we confirm by numerical experiments. 
BibTeX:
@unpublished{KrahmerKuemmerleRauhut18,
author = {Felix Krahmer, Christian Kümmerle, Holger Rauhut},
title = {A Quotient Property for Matrices with HeavyTailed Entries and its Application to NoiseBlind Compressed Sensing},
year = {2018},
url = {https://arxiv.org/abs/1806.04261}
}

M. Fornasier, J. Vybíral and I. Daubechies. Robust and Resource Efficient Identification of Shallow Neural Networks by Fewest Samples, May 2018.
[BibTeX] [arXiv]

BibTeX:
@unpublished{FornasierVybiralDaubechies18,
author = {Massimo Fornasier and Jan Vybíral and Ingrid Daubechies},
title = {Robust and Resource Efficient Identification of Shallow Neural Networks by Fewest Samples},
year = {2018},
url = {https://arxiv.org/abs/1804.01592}
}

M. A. Navascués and P. Massopust. Fractal Convolution: A New Operation between Functions, May 2018.
[BibTeX] [arXiv]

BibTeX:
@unpublished{NavascuesMassopust2018,
author = {Navascu\'es, M. A. and Massopust, P.},
title = {Fractal Convolution: A New Operation between Functions},
year = {2018},
note = {Submitted},
url = {https://arxiv.org/abs/1805.11316}
}

J. Maly and L. Palzer. Analysis of HardThresholding for Distributed Compressed Sensing, May 2018.
[Abstract] [BibTeX] [arXiv]

Abstract A simple hardthresholding operation is shown to be able to recover $L$ signals $\x_1,...,\x_L \in \R^n$ that share a common support of size $s$ from $m = \set{O}(s)$ onebit measurements per signal if $L \ge \log(en/s)$. This result improves the single signal recovery bounds with $m = \set{O}(s\log(en/s))$ measurements in the sense that asymptotically fewer measurements per nonzero entry are needed. Numerical evidence supports the theoretical considerations. 
BibTeX:
@Unpublished{MP2018,
author = {Maly, J. and Palzer, L.},
title = {Analysis of HardThresholding for Distributed Compressed Sensing},
note = {Submitted},
month = may,
year = {2018},
url = {https://arxiv.org/abs/1805.03486}
}

L. Ambrosio, M. Fornasier, M. Morandotti, and S. Savaré. Spatially Inhomogeneous Evolutionary Games, May 2018.
[Abstract] [BibTeX] [arXiv]

Abstract We introduce and study a meanfield model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the interaction between different players and return a feedback on the velocity field guiding their motion.
One of the main novelties of our approach concerns the description of the whole system, which can be represented by an evolving probability measure Σ on an infinite dimensional state space (pairs (x,σ) of position and distribution of strategies). We provide a Lagrangian and a Eulerian description of the evolution, and we prove their equivalence, together with existence, uniqueness, and stability of the solution. As a byproduct of the stability result, we also obtain convergence of the finite agents model to our meanfield formulation, when the number N of the players goes to infinity, and the initial discrete distribution of positions and strategies converge.
To this aim we develop some basic functional analytic tools to deal with interaction dynamics and continuity equations in Banach spaces, that could be of independent interest. 
BibTeX:
@Unpublished{AFMS2018,
author = {Ambrosio, L. and Fornasier, M. and Morandotti, M. and Savar\'e, G.},
title = {Spatially Inhomogeneous Evolutionary Games},
note = {Submitted},
month = may,
year = {2018},
url = {https://arxiv.org/abs/1805.04027}
}

C. Améndola, P. Friz, and B. Strumfels. Varieties of Signature Tensors, April 2018.
[BibTeX] [arXiv]

BibTeX:
@unpublished{AmendolaFrizStrumfels2018,
author = {Améndola, C. and Friz, P. and Strumfels, B.},
title = {Varieties of Signature Tensors},
year = {2018},
note = {Submitted},
url = {https://arxiv.org/abs/1804.08325}
}

J. Hogan and P. Massopust. Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling, April 2018.
[BibTeX] [arXiv]

BibTeX:
@unpublished{HoganMassopust2018,
author = {Hogan, J. and Massopust, P.},
title = {Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling},
year = {2018},
note = {Submitted},
url = {https://arxiv.org/abs/1804.06638}
}

S. Almi and I. Lucardesi. Energy release rate and stress intensity factors in planar elasticity in presence of smooth cracks, 2018.
[BibTeX]

BibTeX:
@unpublished{AlmiLucardesi2018,
author = {Almi, S. and Lucardesi, I.},
title = {Energy release rate and stress intensity factors in planar elasticity in presence of smooth cracks},
year = {2018},
note = {Submitted}
}

M. Fornasier, S. Lisini, C. Orrieri and G. Savaré. Meanfield optimal control as Gammalimit of finite agent controls, March 2018.
[Abstract] [BibTeX] [arXiv]

Abstract This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of continuitytype without diffusion, governing the dynamics of the probability distribution of the agent population. We derive existence of optimal controls in a measuretheoretical setting as natural limits of finite agent optimal controls without any assumption on the regularity of control competitors. In particular, we prove the consistency of meanfield optimal controls with corresponding underlying finite agent ones. The results follow from a Γconvergence argument constructed over the meanfield limit, which stems from leveraging the superposition principle. 
BibTeX:
@unpublished{FLOS18,
author = {Fornasier, M. and Lisini, S. and Orrieri, C. and Savaré, G.},
title = {Meanfield optimal control as Gammalimit of finite agent controls},
year = {2018},
url = {https://arxiv.org/abs/1803.04689}
}

M. Fornasier, J. Maly and V. Naumova. Sparse PCA from Inaccurate and Incomplete Measurements, January 2018.
[Abstract] [BibTeX] [arXiv]

Abstract We consider the problem of recovering an unknown effectively sparse lowrank matrix from a small set of incomplete and inaccurate linear measurements of the form y=(X)+η, where η is an {\it ineliminable} noise. This problem encompasses and fuses two important classes of machine learning and signal processing challenges: sparse principal component analysis and compressed sensing. More specifically, we aim at recovering lowrankR matrices with effectively (s1,s2)sparse nonorthogonal rank1 decompositions. We describe an optimization problem for matrix recovery under the considered model and propose a novel algorithm, called {\it \textbf{A}lternating \textbf{T}ikhonov regularization and \textbf{Las}so} (ATLAS2,1), to solve it. The algorithm is based on a multipenalty regularization, which is able to leverage both structures (lowrankness and sparsity) simultaneously. The algorithm is a fast first order method, and straightforward to implement. We prove global convergence for {\it any} linear measurement model to stationary points and local convergence to global minimizers of the multipenalty objective functional. Global minimizers balance effective sparsity of their rank1 decompositions and the fidelity to data, up to noise level. By adapting the concept of restricted isometry property from compressed sensing to our novel model class, we prove error bounds between global minimizers and ground truth, up to noise level, from a number of subgaussian measurements scaling as R(s1+s2), up to logfactors in the dimension, and relativetodiameter distortion. Simulation results demonstrate both the accuracy and efficacy of the algorithm, as well as its superiority to the stateoftheart algorithms in strong noise regimes and for matrices, whose singular vectors do not possess exact (joint) sparse support. 
BibTeX:
@unpublished{FMN18,
author = {Fornasier, M. and Maly, J. and Naumova, V.},
title = {Sparse PCA from Inaccurate and Incomplete Measurements},
year = {2018},
url = {https://arxiv.org/abs/1801.06240}
}

S. Almi, S. Belz and M. Negri. Convergence of discrete and continuous unilateral flows for AmbrosioTortorelli energies and application to mechanics, 2017.
[BibTeX]

BibTeX:
@unpublished{AlmiBelzNegri2017,
author = {Almi, S. and Belz, S. and Negri, M.},
title = {Convergence of discrete and continuous unilateral flows for AmbrosioTortorelli energies and application to mechanics},
year = {2017},
note = {Submitted}
}

S. Almi and S. Belz. Consistent finitedimensional approximation of phasefield models of fracture, July 2017.
[BibTeX] [arXiv]

BibTeX:
@unpublished{AlmiBelz2017,
author = {Almi, S. and Belz, S.},
title = {Consistent finitedimensional approximation of phasefield models of fracture},
year = {2017},
note = {Submitted},
url = {https://arxiv.org/abs/1707.00578}
}

P. Jung, F. Krahmer and D. Stöger. Blind Demixing and Deconvolution at NearOptimal Rate, April 2017.
[Abstract] [BibTeX]

Abstract We consider simultaneous blind deconvolution of r source signals from its noisy superposition, a problem also referred to blind demixing and deconvolution. This signal processing problem occurs in the context of the Internet of Things where a massive number of sensors sporadically communicate only short messages over unknown channels. We show that robust recovery of message and channel vectors can be achieved via convex optimization when random linear encoding using i.i.d. complex Gaussian matrices is used at the devices and the number of required measurements at the receiver scales with the degrees of freedom of the overall estimation problem. Since the scaling is linear in r our result significantly improves over recent works. 
BibTeX:
@unpublished{JKS17,
author = {Jung, P. and Krahmer, F. and Stöger, D.},
title = {Blind Demixing and Deconvolution at NearOptimal Rate},
year = {2017},
url = {https://arxiv.org/abs/1704.04178}
}

J.M. Feng, F. Krahmer and R. Saab. Quantized Compressed Sensing for Partial Random Circulant Matrices, February 2017.
[Abstract] [BibTeX]

Abstract We provide the first analysis of a nontrivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at random, without replacement, from a circulant matrix generated by a random subgaussian vector. We quantize the measurements using stable, possibly onebit, SigmaDelta schemes, and use a reconstruction method based on convex optimization. We show that the part of the reconstruction error due to quantization decays polynomially in the number of measurements. This is in line with analogous results on SigmaDelta quantization associated with random Gaussian or subgaussian matrices, and significantly better than results associated with the widely assumed memoryless scalar quantization. Moreover, we prove that our approach is stable and robust; i.e., the reconstruction error degrades gracefully in the presence of nonquantization noise and when the underlying signal is not strictly sparse. The analysis relies on results concerning subgaussian chaos processes as well as a variation of McDiarmid's inequality. 
BibTeX:
@unpublished{FKS17,
author = {Feng, J.M. and Krahmer, F. and Saab, R.},
title = {Quantized Compressed Sensing for Partial Random Circulant Matrices},
year = {2017},
url = {https://arxiv.org/abs/1702.04711}
}

M. Ehler and F. Filbir. Metric entropy, nwidths, and sampling of functions on manifolds, 2017.
[BibTeX] [arXiv]

BibTeX:
@unpublished{EF16,
author = {Ehler, M. and Filbir, F.},
title = {Metric entropy, nwidths, and sampling of functions on manifolds},
year = {2017},
url = {https://arxiv.org/abs/1311.1393}
}

G. Albi, M. Fornasier and D. Kalise. A Boltzmann approach to meanfield sparse feedback control, November 2016.
[BibTeX] [arXiv]

BibTeX:
@Unpublished{AFK16,
author = {Giacomo Albi and Massimo Fornasier and Dante Kalise},
title = {A Boltzmann approach to meanfield sparse feedback control},
year = {2016},
annote = {Submitted Preprints},
annoten = {1},
file = {:ifac_AFK_final3.pdf:PDF},
timestamp = {2016.11.15},
url = {https://arxiv.org/abs/1611.03988},
}

E. de Vito, M. Fornasier and V. Naumova. A Machine Learning Approach to Optimal Tikhonov Regularisation I: Affine Manifolds, October 2016.
[Abstract] [BibTeX] [arXiv]

Abstract Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the parameter from given noisy data without relying either on a priori knowledge of the solution or on the noise level. In this paper we propose a novel method based on supervised machine learning to approximate the highdimensional function, mapping noisy data into a good approximation to the optimal Tikhonov regularization parameter. Our assumptions are that solutions of the inverse problem are statistically distributed in a concentrated manner on (lowerdimensional) linear subspaces and the noise is subgaussian. One of the surprising facts is that the number of previously observed examples for the supervised learning of the optimal parameter mapping scales at most linearly with the dimension of the solution subspace. We also provide explicit error bounds on the accuracy of the approximated parameter and the corresponding regularization solution. Even though the results are more of theoretical nature, we present a recipe for the practical implementation of the approach and provide numerical experiments confirming the theoretical results. We also outline interesting directions for future research with some preliminary results, confirming their feasibility. 
BibTeX:
@unpublished{DVFN16,
author = {Ernesto de Vito and Massimo Fornasier and Valeriya Naumova},
title = {A Machine Learning Approach to Optimal Tikhonov Regularisation I: Affine Manifolds},
year = {2016},
url = {https://arxiv.org/abs/1610.01952}
}

Y.P. Choi and S. Salem. Propagation of chaos for aggregation equations with noflux boundary conditions and sharp sensing zones, October 2016.
[BibTeX]

BibTeX:
@unpublished{ChoiSalem16,
author = {Y.P. Choi and S. Salem},
title = {Propagation of chaos for aggregation equations with noflux boundary conditions and sharp sensing zones},
year = {2016},
url = {https://arxiv.org/pdf/1610.03261v1.pdf}
}

M. F. Barnsley, M. Hegland and P. Massopust. Selfreferential functions, October 2016.
[BibTeX]

BibTeX:
@unpublished{BHM6,
author = {Barnsley, Michael F., Hegland, Markus, and Massopust, Peter},
title = {Selfreferential functions},
year = {2016},
url = {http://arxiv.org/abs/1610.01369}
}

G. Albi, Y.P. Choi, M. Fornasier and D. Kalise. Mean Field Control Hierarchy, August 2016.
[BibTeX]

BibTeX:
@unpublished{ACFK16,
author = {Giacomo Albi and YoungPil Choi and Massimo Fornasier and Dante Kalise},
title = {Mean Field Control Hierarchy},
year = {2016}
}

M. Fornasier. Learning and sparse control of multiagent systems, In Proc. 7thECM, pp. 131, 2016.
[BibTeX]

BibTeX:
@inproceedings{F7thECM,
author = {Massimo Fornasier},
title = {Learning and sparse control of multiagent systems},
booktitle = {Proc. 7thECM},
year = {2016},
pages = {131}
}

F. Filbir and K. Schröder. Exact Recovery of Discrete Measures from Wigner DMoments, June 2016.
[BibTeX]

BibTeX:
@unpublished{FS16,
author = {Filbir, F. and Schröder, K.},
title = {Exact Recovery of Discrete Measures from Wigner DMoments},
year = {2016},
url = {https://arxiv.org/abs/1606.05306}
}

F. Krahmer and Y. Liu. Phase Retrieval Without SmallBall Probability Assumptions, April 2016.
[BibTeX]

BibTeX:
@unpublished{KL16,
author = {Felix Krahmer and YiKai Liu},
title = {Phase Retrieval Without SmallBall Probability Assumptions},
year = {2016},
url = {http://arxiv.org/abs/1604.07281}
}

G. Albi and L. Pareschi. Selective modelpredictive control for flocking systems, March 2016.
[BibTeX]

BibTeX:
@unpublished{2016arXiv160305012A,
author = {Albi, Giacomo and Pareschi, Lorenzo},
title = {Selective modelpredictive control for flocking systems},
year = {2016},
url = {http://arxiv.org/abs/1603.05012}
}

M. Eller and M. Fornasier. Rotation Invariance in Exemplarbased Image Inpainting, Radon Series on Computational and Applied Mathematics, 2015.
[BibTeX]

BibTeX:
@incollection{EF_Chapter,
author = {M. Eller and M. Fornasier},
title = {Rotation Invariance in Exemplarbased Image Inpainting},
publisher = {Radon Series on Computational and Applied Mathematics},
year = {2015}
}

M. Bongini, M. Fornasier, F. Rossi and F. Solombrino. MeanField Pontryagin Maximum Principle, April 2015.
[BibTeX] [arXiv]

BibTeX:
@unpublished{BFRS15,
author = {Bongini, M. and Fornasier, M. and Rossi, F. and Solombrino, F. },
title = {MeanField Pontryagin Maximum Principle},
year = {2015},
url = {https://arxiv.org/abs/1504.02236}
}

M. Hansen. A new embedding result for Kondratiev spaces and application to adaptive approximation of elliptic PDEs, submitted to Analysis and Applications, 2014.
[BibTeX]

BibTeX:
@unpublished{H14,
author = {Markus Hansen},
title = {A new embedding result for Kondratiev spaces and application to adaptive approximation of elliptic PDEs},
journal = {submitted to Analysis and Applications},
year = {2014}
}

M. Fornasier and F. Vecil. Numerical analysis on CuckerSmale collective behavior models, 2013.
[BibTeX]

BibTeX:
@unpublished{FV13,
author = {Fornasier, Massimo and Vecil, Francesco},
title = {Numerical analysis on CuckerSmale collective behavior models},
year = {2013}
}


back to top 
Refereed Journal Articles 
to appear 
J.A. Carrillo, Y.P. Choi, M. Hauray and S. Salem. Meanfield limit for collective behavior models with sharp sensitivity regions, J. Eur. Math. Soc.:132, to appear.
[BibTeX] [arXiv]

BibTeX:
@article{2015arXiv151002315C,
author = {Carrillo, J. A. and Choi, Y.P. and Hauray, M. and Salem, S.},
title = {Meanfield limit for collective behavior models with sharp sensitivity regions},
journal = {J. Eur. Math. Soc.},
year = {to appear},
pages = {132},
url = {http://arxiv.org/pdf/1510.02315v2.pdf},
doi = {10.4171/JEMS/832}
}

2018 
C. Kümmerle and J. Sigl. Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery, Journal of Machine Learning Research, 19(47):1−49, 2018.
[Abstract] [BibTeX] [arXiv] [Code ^{}]

Abstract We propose a new iteratively reweighted least squares (IRLS) algorithm for the recovery of a matrix X ∊ ℂ^(d_1× d_2) of rank r ≪ min(d_1,d_2) from incomplete linear observations, solving a sequence of low complexity linear problems. The easily implementable algorithm, which we call harmonic mean iteratively reweighted least squares (HMIRLS), optimizes a nonconvex Schattenp quasinorm penalization to promote lowrankness and carries three major strengths, in particular for the matrix completion setting. First, the algorithm converges globally to the lowrank matrix for relevant, interesting cases, for which any other (non)convex stateoftheart optimization approach fails the recovery. Secondly, HMIRLS exhibits an empirical recovery probability close to 100% even for a number of measurements very close to the theoretical lower bound r (d_1 +d_2 r), i.e., already for significantly fewer linear observations than any other tractable approach in the literature. Thirdly, HMIRLS exhibits a locally superlinear rate of convergence (of order 2p) if the linear observations fulfill a suitable null space property. While for the first two properties we have so far only strong empirical evidence, we prove the third property as our main theoretical result. 
BibTeX:
@article{JMLR:v19:17244,
author = {Christian K{\"u}mmerle and Juliane Sigl},
title = {Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery},
journal = {Journal of Machine Learning Research},
year = {2018},
volume = {19},
number = {47},
pages = {149},
url = {http://jmlr.org/papers/v19/17244.html}
}

C. Améndola, N. Bliss, I. Burke, C.R. Gibbons, M. Helmer, S. Hoşten, E.D. Nash, J.I. Rodriguez, and D. Smolkin. The maximum likelihood degree of toric varieties, Journal of Symbolic Computation, Online April 11, 2018.
[Abstract] [BibTeX] [URL]

Abstract We study the maximum likelihood (ML) degree of toric varieties, known as discrete exponential models in statistics. By introducing scaling coefficients to the monomial parameterization of the toric variety, one can change the ML degree. We show that the ML degree is equal to the degree of the toric variety for generic scalings, while it drops if and only if the scaling vector is in the locus of the principal Adeterminant. We also illustrate how to compute the ML estimate of a toric variety numerically via homotopy continuation from a scaled toric variety with low ML degree. Throughout, we include examples motivated by algebraic geometry and statistics. We compute the ML degree of rational normal scrolls and a large class of Veronesetype varieties. In addition, we investigate the ML degree of scaled Segre varieties, hierarchical loglinear models, and graphical models. 
BibTeX:
@unpublished{ABBGHHNRS2018,
author = {Am\'endola, C. and Bliss, N. and Burke, I. and Gibbons, C.R. and Helmer, M. and Ho\c{s}ten, S. and Nash, E.D. and Rodriguez, J.I. and Smolkin, D.},
title = {The maximum likelihood degree of toric varieties},
journal = {Journal of Symbolic Computation},
year = {2018},
url = {https://doi.org/10.1016/j.jsc.2018.04.016}
}

P. Massopust. Local Fractal Interpolation On Unbounded Domains, Proc. Edinb. Math. Soc. (2), 61(1), 151167, 2018.
[BibTeX] [arXiv]

BibTeX:
@article{Massopust2018,
author = {Massopust, P.},
title = {Local Fractal Interpolation On Unbounded Domains},
journal = {Proc. Edinb. Math. Soc. (2)},
year = {2018},
volume = {61},
number = {1},
pages = {151167},
url = {https://arxiv.org/abs/1508.03198},
doi = {10.1017/S0013091517000268}
}

G. Carita, J. Matias, M. Morandotti and D.R. Owen. Dimension reduction in the context of structured deformations. J. Elast., Online January 19, 2018.
[Abstract] [BibTeX] [URL]

Abstract In this paper we apply both the procedure of dimension reduction and the incorporation of structured deformations to a threedimensional continuum in the form of a thinning domain. We apply the two processes one after the other, exchanging the order, and so obtain for each order both a relaxed bulk and a relaxed interfacial energy. Our implementation requires some substantial modifications of the two relaxation procedures. For the specific choice of an initial energy including only the surface term, we compute the energy densities explicitly and show that they are the same, independent of the order of the relaxation processes. Moreover, we compare our explicit results with those obtained when the limiting process of dimension reduction and of passage to the structured deformation is carried out at the same time. We finally show that, in a portion of the common domain of the relaxed energy densities, the simultaneous procedure gives an energy strictly lower than that obtained in the twostep relaxations. 
BibTeX:
@unpublished{CMMO17,
author = {Carita, G. and Matias, J. and Morandotti, M. and Owen, D. R.},
title = {Dimension reduction in the context of structured deformations},
journal = {J. Elast},
year = {2018},
url = {https://link.springer.com/article/10.1007%2Fs1065901896709}
}

B. Bringmann, D. Cremers, F. Krahmer and M. Moeller. The Homotopy Method Revisited: Computing Solution Paths of ℓ1Regularized Problems, Math. Comp., 82(313):23432364, 2018.
[BibTeX] [arXiv]

BibTeX:
@article{BCKM18,
author = {Bringmann, B. and Cremers, D. and Krahmer, F. and Moeller, M.},
title = {The Homotopy Method Revisited: Computing Solution Paths of ℓ1Regularized Problems},
journal = {Math. Comp.},
year = {2018},
volume = {82},
number = {313},
pages = {23432364},
url = {http://www.ams.org/journals/mcom/201887313/S002557182017032877/},
doi = {10.1090/mcom/3287}
}

2017 
M. Bongini and G. Buttazzo. Optimal Control Problems in Transport Dynamics, Math. Mod. Meth. Appl. Sci., 27(03):427451, 2017.
[BibTeX] [arXiv] [.pdf]

BibTeX:
@article{BB16,
author = {Bongini, Mattia and Buttazzo, Giuseppe},
title = {Optimal Control Problems in Transport Dynamics},
journal = {Math. Mod. Meth. Appl. Sci.},
year = {2017},
volume = {27},
number = {03},
pages = {427451},
url = {https://arxiv.org/pdf/1609.07323.pdf},
doi = {10.1142/S0218202517500063}
}

Y.P. Choi. Finitetime blowup phenomena of Vlasov/NavierStokes equations and related systems, J. Math. Pures Appl., 108(6):9911021, 2017.
[BibTeX] [arXiv]

BibTeX:
@article{CYP16_3,
author = {Y.P. Choi},
title = {Finitetime blowup phenomena of Vlasov/NavierStokes equations and related systems},
journal = {J. Math. Pures Appl.},
year = {2017},
volume = {108},
number = {6},
pages = {9911021},
url = {http://arxiv.org/pdf/1606.07158.pdf},
doi = {10.1016/j.matpur.2017.05.019}
}

T. Hudson and M. Morandotti. Properties of screw dislocation dynamics: time estimates on boundary and interior collisions, SIAM J. Appl. Math., 77(5) (2017), 16781705.
[Abstract] [BibTeX] [arXiv] [URL]

Abstract In this paper, the dynamics of a system of a finite number of screw dislocations is studied. Under the assumption of antiplane linear elasticity, the twodimensional dynamics is determined by the renormalised energy. The interaction of one dislocation with the boundary and of two dislocations of opposite Burgers moduli are analysed in detail and estimates on the collision times are obtained. Some exactly solvable cases and numerical simulations show agreement with the estimates obtained. 
BibTeX:
@article{HM17a,
author = {Hudson, T. and Morandotti, M.},
title = {Properties of screw dislocation dynamics: time estimates on boundary and interior collisions},
journal = {SIAM J. Appl. Math.},
year = {2017},
volume = {77},
number = {5},
pages = {16781705},
url = {https://doi.org/10.1137/17M1119974}
}

J.A. Hogan and P. Massopust. Quaternionic BSplines, J. Approx. Th., 224:4365, 2017.
[BibTeX] [arXiv]

BibTeX:
@article{HM17,
author = {Hogan, Jeffrey A. and Massopust, Peter},
title = {Quaternionic BSplines},
journal = {J. Approx. Th.},
year = {2017},
volume = {224},
pages = {4365},
url = {http://arxiv.org/abs/1608.08428},
doi = {10.1016/j.jat.2017.09.003}
}

P.R. Massopust and P.J. Van Fleet. Fractional Cone Splines and Hex Splines, Rocky Mountain J. Math., 47(5):16551691, 2017.
[Abstract] [BibTeX] [arXiv] [.pdf]

Abstract We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain sdimensional meshes and include as special cases the threedirectional box splines article:condat and hex splines article:vandeville previously considered by Condat, Van De Ville et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex Bsplines defined in article:ub,article:fbu and investigated in, e.g., article:fm,article:mf. Explicit time domain representations are derived for these splines on 3directional meshes. We present some properties of these two multivariate spline families such as recurrence, decay and refinement. Finally it is shown that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span. 
BibTeX:
@article{MF17,
author = {Massopust, Peter R and Van Fleet, Patrick J},
title = {Fractional Cone Splines and Hex Splines},
journal = {Rocky Mountain J. Math.},
year = {2017},
volume = {47},
number = {5},
pages = {16551691},
url = {http://arxiv.org/abs/1504.00546}
}

M. Morandotti. Boundary Behavior and Confinement of Screw Dislocations, MRS Advances, 2(48):2633–2638, Materials Research Society, 2017.
[Abstract] [BibTeX]

Abstract In this note we discuss two aspects of screw dislocations dynamics: their behavior near the boundary and a way to confine them inside the material. In the former case, we obtain analytical results on the estimates of collision times (one dislocation with the boundary and two dislocations with opposite Burgers vectors with each other); numerical evidence is also provided. In the latter, we obtain analytical results stating that, under imposing a certain type of boundary conditions, it is energetically favorable for dislocations to remain confined inside the domain. 
BibTeX:
@article{Morandotti172,
author = {Morandotti, Marco},
title = {Boundary Behavior and Confinement of Screw Dislocations},
journal = {MRS Advances},
publisher = {Materials Research Society},
year = {2017},
volume = {2},
number = {48},
pages = {2633–2638},
doi = {10.1557/adv.2017.386}
}

A.C. Barroso, J. Matias, M. Morandotti and D.R. Owen. Secondorder structured deformations: relaxation, integral representation and applications, Arch. Rational Mech. Anal.(225):10251072, 2017.
[Abstract] [BibTeX] [arXiv]

Abstract Secondorder structured deformations of continua provide an extension of the multiscale geometry of firstorder structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral representation for a relaxed energy functional in the setting of secondorder structured deformations. Our derivation covers inhomogeneous initial energy densities (i.e., with explicit dependence on the position); finally, we provide explicit formulas for bulk relaxed energies as well as anticipated applications. 
BibTeX:
@article{BMMO16,
author = {Barroso, A. C. and Matias, J. and Morandotti, M. and Owen, D. R.},
title = {Secondorder structured deformations: relaxation, integral representation and applications},
journal = {Arch. Rational Mech. Anal.},
year = {2017},
number = {225},
pages = {10251072},
url = {https://arxiv.org/pdf/1607.02311},
doi = {10.1007/s0020501711205}
}

Y.P. Choi and J. Haskovec. CuckerSmale model with normalized communication weights and time delay, Kinetic and Related Models, 10(4):10111033, 2017.
[Abstract] [BibTeX] [arXiv]

Abstract Abstract We study a CuckerSmaletype system with time delay in which agents interact with each other through normalized communication weights. We construct a Lyapunov functional for the system and provide sufficient conditions for asymptotic flocking, i.e., convergence to a common velocity vector. We also carry out a rigorous limit passage to the meanfield limit of the particle system as the number of particles tends to infinity. For the resulting Vlasovtype equation we prove the existence, stability and largetime behavior of measurevalued solutions. This is, to our best knowledge, the first such result for a Vlasovtype equation with time delay. We also present numerical simulations of the discrete system with few particles that provide further insights into the flocking and oscillatory behaviors of the particle velocities depending on the size of the time delay. 
BibTeX:
@article{CH16,
author = {YoungPil Choi and Jan Haskovec},
title = {CuckerSmale model with normalized communication weights and time delay},
journal = {Kinetic and Related Models},
year = {2017},
volume = {10},
number = {4},
pages = {10111033},
url = {http://arxiv.org/abs/1608.06747},
doi = {10.3934/krm.2017040}
}

J.A. Carrillo, Y.P. Choi, P.B. Mucha and J. Peszek. Sharp conditions to avoid collisions in singular Cucker–Smale interactions, Nonlinear Anal. Real World Appl., 37:317  328, 2017.
[Abstract] [BibTeX] [arXiv]

Abstract We consider the Cucker–Smale flocking model with a singular communication weight ψ(s)=s−α with α>0. We provide a critical value of the exponent α in the communication weight leading to global regularity of solutions or finitetime collision between particles. For α≥1, we show that there is no collision between particles in finite time if they are placed in different positions initially. For α≥2 we investigate a version of the Cucker–Smale model with expanded singularity i.e. with weight ψδ(s)=(s−δ)−α, δ≥0. For such model we provide a uniform with respect to the number of particles estimate that controls the δdistance between particles. In case of δ=0 it reduces to the estimate of collision avoidance. 
BibTeX:
@article{CCMP16,
author = {José A. Carrillo and YoungPil Choi and Piotr B. Mucha and Jan Peszek},
title = {Sharp conditions to avoid collisions in singular Cucker–Smale interactions},
journal = {Nonlinear Anal. Real World Appl.},
year = {2017},
volume = {37},
pages = {317  328},
url = {http://arxiv.org/pdf/1609.03447},
doi = {10.1016/j.nonrwa.2017.02.017}
}

M. Bongini, M. Fornasier, M. Hansen and M. Maggioni. Inferring Interaction Rules from Observations of Evolutive Systems I: The Variational Approach, Math. Models Methods Appl. Sci., 27(05):909951, 2017.
[BibTeX] [arXiv] [.pdf]

BibTeX:
@article{BFHM16,
author = {Mattia Bongini and Massimo Fornasier and Markus Hansen and Mauro Maggioni},
title = {Inferring Interaction Rules from Observations of Evolutive Systems I: The Variational Approach},
journal = {Math. Models Methods Appl. Sci.},
year = {2017},
volume = {27},
number = {05},
pages = {909951},
url = {http://arxiv.org/abs/1602.00342},
doi = {10.1142/S0218202517500208}
}

G. Albi, L. Pareschi and M. Zanella. Opinion dynamics over complex networks: Kinetic modelling and numerical methods, Kinetic and Related Models, 10(1):132, 2017.
[Abstract] [BibTeX] [arXiv]

Abstract Abstract In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents' distribution over the evolving network is considered which combines an opinion update based on binary interactions between agents with a dynamic creation and removal process of new connections. The number of connections of each agent influences the spreading of opinions in the network but also the way connections are created is influenced by the agents' opinion. The evolution of the network of connections is studied by showing that its asymptotic behavior is consistent both with Poisson distributions and truncated powerlaws. In order to study the large time behavior of the opinion dynamics a mean field description is derived which allows to compute exact stationary solutions in some simplified situations. Numerical methods which are capable to describe correctly the large time behavior of the system are also introduced and discussed. Finally, several numerical examples showing the influence of the agents' number of connections in the opinion dynamics are reported. 
BibTeX:
@article{APZ16,
author = {Giacomo Albi and Lorenzo Pareschi and Mattia Zanella},
title = {Opinion dynamics over complex networks: Kinetic modelling and numerical methods},
journal = {Kinetic and Related Models},
year = {2017},
volume = {10},
number = {1},
pages = {132},
url = {http://arxiv.org/abs/1604.00421},
doi = {10.3934/krm.2017001}
}

P. Massopust, B. Forster and O. Christensen. Fractional and complex pseudosplines and the construction of Parseval frames, Appl. Math. Comput., 314:1224, 2017.
[Abstract] [BibTeX] [arXiv]

Abstract Abstract Pseudosplines of integer order (m, â„“) were introduced by Daubechies, Han, Ron, and Shen as a family which allows interpolation between the classical Bsplines and the Daubechiesâ€™ scaling functions. The purpose of this paper is to generalize the pseudosplines to fractional and complex orders (z, â„“) with Î± â‰” Reâ€‰z â‰¥ 1. This allows increased flexibility in regard to smoothness: instead of working with a discrete family of functions from Cm, m âˆˆ N 0 , one uses a continuous family of functions belonging to the HÃ¶lder spaces C Î± âˆ’ 1 . The presence of the imaginary part of z allows for direct utilization in complex transform techniques for signal and image analyses. We also show that in analogue to the integer case, the generalized pseudosplines lead to constructions of Parseval wavelet frames via the unitary extension principle. The regularity and approximation order of this new class of generalized splines is also discussed. 
BibTeX:
@article{MFO17,
author = {Peter Massopust and Brigitte Forster and Ole Christensen},
title = {Fractional and complex pseudosplines and the construction of Parseval frames},
journal = {Appl. Math. Comput.},
year = {2017},
volume = {314},
pages = {1224},
url = {http://arxiv.org/abs/1602.08580},
doi = {10.1016/j.amc.2017.06.023}
}

M. Kech and F. Krahmer. Optimal Injectivity Conditions for Bilinear Inverse Problems with Applications to Identifiability of Deconvolution Problems, SIAM Journal on Applied Algebra and Geometry, 1(1):2037, 2017.
[Abstract] [BibTeX] [arXiv]

Abstract We study identifiability for bilinear inverse problems under sparsity and subspace constraints. We show that, up to a global scaling ambiguity, almost all such maps are injective on the set of pairs of sparse vectors if the number of measurements m exceeds 2(s_1+s_2)2, where s_1 and s_2 denote the sparsity of the two input vectors, and injective on the set of pairs of vectors lying in known subspaces of dimensions n_1 and n_2 if m≥ 2(n_1+n_2)4. We also prove that both these bounds are tight in the sense that one cannot have injectivity for a smaller number of measurements. Our proof technique draws from algebraic geometry. As an application we derive optimal identifiability conditions for the deconvolution problem, thus improving on recent work of Li, Lee, and Bresler [Y. Li, K. Lee, and Y. Bresler, Identifiability and Stability in Blind Deconvolution under Minimal Assumptions, preprint, https://arxiv.org/abs/1507.01308, 2015]. 
BibTeX:
@article{KK17,
author = {Michael Kech and Felix Krahmer},
title = {Optimal Injectivity Conditions for Bilinear Inverse Problems with Applications to Identifiability of Deconvolution Problems},
journal = {SIAM Journal on Applied Algebra and Geometry},
year = {2017},
volume = {1},
number = {1},
pages = {2037},
url = {http://arxiv.org/abs/1603.07316},
doi = {10.1137/16M1067469}
}

A. Schindele, P. Massopust and B. Forster. Multigrid Convergence for the MDCA Curvature Estimator, Journal of Mathematical Imaging and Vision, 57(3):423438, 2017.
[Abstract] [BibTeX] [.pdf]

Abstract We consider the problem of estimating the curvature profile along the boundaries of digital objects in segmented blackandwhite images. We start with the curvature estimator proposed by Roussillon et al. which is based on the calculation of maximal digital circular arcs (MDCAs). We extend this estimator to the $$backslashlambda $$ λ MDCA curvature estimator that considers several MDCAs for each boundary pixel and is therefore smoother than the classical MDCA curvature estimator. We prove an explicit order of convergence result for convex subsets in $$backslashmathbb R^2$$ R 2 with positive, continuous curvature profile. In addition, we evaluate the curvature estimator on various objects with known curvature profile. We show that the observed order of convergence is close to the theoretical limit of $$backslashmathcal Obackslashleft( h^backslashfrac13backslashright) $$ O h 1 3 as $$hbackslashrightarrow 0^+$$ h textrightarrow 0 + . Furthermore, we establish that the $$backslashlambda $$ λ MDCA curvature estimator outperforms the MDCA curvature estimator, especially in the neighborhood of corners. 
BibTeX:
@article{SMF17,
author = {Schindele, Andreas and Massopust, Peter and Forster, Brigitte},
title = {Multigrid Convergence for the MDCA Curvature Estimator},
journal = {Journal of Mathematical Imaging and Vision},
year = {2017},
volume = {57},
number = {3},
pages = {423438},
doi = {10.1007/s1085101606851}
}

M. Artina, F. Cagnetti, M. Fornasier and F. Solombrino. Linearly constrained evolutions of critical points and an application to cohesive fractures, Math. Models Methods Appl. Sci., 27(02):231290, 2017.
[Abstract] [BibTeX] [arXiv] [.pdf]

Abstract We introduce a novel constructive approach to define time evolution of critical points of an energy functional. Our procedure, which is different from other more established approaches based on viscosity approximations in infinite dimension, is prone to efficient and consistent numerical implementations, and allows for an existence proof under very general assumptions. We consider in particular rather nonsmooth and nonconvex energy functionals, provided the domain of the energy is finite dimensional. Nevertheless, in the infinite dimensional case study of a cohesive fracture model, we prove a consistency theorem of a discretetocontinuum limit. We show that a quasistatic evolution can be indeed recovered as a limit of evolutions of critical points of finite dimensional discretizations of the energy, constructed according to our scheme. To illustrate the results, we provide several numerical experiments both in one and two dimensions. These agree with the crack initiation criterion, which states that a fracture appears only when the stress overcomes a certain threshold, depending on the material. 
BibTeX:
@article{ACFS17,
author = {Artina, M. and Cagnetti, F. and Fornasier, M. and Solombrino, F.},
title = {Linearly constrained evolutions of critical points and an application to cohesive fractures},
journal = {Math. Models Methods Appl. Sci.},
year = {2017},
volume = {27},
number = {02},
pages = {231290},
url = {http://arxiv.org/abs/1508.02965},
doi = {10.1142/S0218202517500014}
}

M. Storath, L. Demaret and P. Massopust. Signal analysis based on complex wavelet signs, Appl. Comput. Harmon. Anal., 42(2):199  223, 2017.
[Abstract] [BibTeX]

Abstract We propose a signal analysis tool based on the sign (or the phase) of complex wavelet coefficients, which we call a signature. The signature is defined as the finescale limit of the signs of a signal's complex wavelet coefficients. We show that the signature equals zero at sufficiently regular points of a signal whereas at salient features, such as jumps or cusps, it is nonzero. At such feature points, the orientation of the signature in the complex plane can be interpreted as an indicator of local symmetry and antisymmetry. We establish that the signature rotates in the complex plane under fractional Hilbert transforms. We show that certain random signals, such as white Gaussian noise and Brownian motions, have a vanishing signature. We derive an appropriate discretization and show the applicability to signal analysis. 
BibTeX:
@article{SDM17,
author = {Martin Storath and Laurent Demaret and Peter Massopust},
title = {Signal analysis based on complex wavelet signs},
journal = {Appl. Comput. Harmon. Anal.},
year = {2017},
volume = {42},
number = {2},
pages = {199  223},
doi = {10.1016/j.acha.2015.08.005}
}

D. Gross, F. Krahmer and R. Kueng. Improved Recovery Guarantees for Phase Retrieval from Coded Diffraction Patterns, Appl. Comput. Harmon. Anal., 42(1):37  64, 2017.
[Abstract] [BibTeX] [arXiv]

Abstract In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex optimization. We provide recovery guarantees which require O ( log^2 d ) different diffraction patterns, thus improving on recent results by Candès et al. [1], which demand O ( log ^4 d ) different patterns. 
BibTeX:
@article{GKK15,
author = {D. Gross and F. Krahmer and R. Kueng},
title = {Improved Recovery Guarantees for Phase Retrieval from Coded Diffraction Patterns},
journal = {Appl. Comput. Harmon. Anal.},
year = {2017},
volume = {42},
number = {1},
pages = {37  64},
url = {http://arxiv.org/abs/1402.6286},
doi = {10.1016/j.acha.2015.05.004}
}

2016 
G. Albi, M. Bongini, E. Cristiani and D. Kalise. Invisible Control of SelfOrganizing Agents Leaving Unknown Environments, SIAM J. Appl. Math., 76(4):16831710, 2016.
[BibTeX] [arXiv] [.pdf]

BibTeX:
@article{ABCK16,
author = {Giacomo Albi and Mattia Bongini and Emiliano Cristiani and Dante Kalise},
title = {Invisible Control of SelfOrganizing Agents Leaving Unknown Environments},
journal = {SIAM J. Appl. Math.},
year = {2016},
volume = {76},
number = {4},
pages = {16831710},
url = {http://arxiv.org/abs/1504.04064},
doi = {10.1137/15M1017016}
}

J. Sigl. Nonlinear residual minimization by iteratively reweighted least squares, Computational Optimization and Applications, 64(3):755792, 2016.
[Abstract] [BibTeX] [.pdf]

Abstract In this paper we address the numerical solution of minimal norm residuals of nonlinear equations in finite dimensions. We take particularly inspiration from the problem of finding a sparse vector solution of phase retrieval problems by using greedy algorithms based on iterative residual minimizations in the pnorm, for 1≤ p≤ 2%. Due to the mild smoothness of the problem, especially for p → 1$, we develop and analyze a generalized version of iteratively reweighted least squares (IRLS). This simple and efficient algorithm performs the solution of optimization problems involving nonquadratic possibly nonconvex and nonsmooth cost functions, which can be transformed into a sequence of common least squares problems. The latter can be tackled eventually by more efficient numerical optimization methods. While its analysis has been by now developed in many different contexts (e.g., for sparse vector, lowrank matrix optimization, and for the solution of PDE involving pLaplacians) when the model equation is linear, no results are up to now provided in case of nonlinear ones. We address here precisely the convergence and the rate of error decay of IRLS for such nonlinear problems. The analysis of the convergence of the algorithm is based on its reformulation as an alternating minimization of an energy functional. In fact its main variables are the competitors to solutions of the intermediate reweighted least squares problems and their weights. Under a specific condition of coercivity often verified in practice and assumptions of local convexity, we are able to show convergence of IRLS to minimizers of the nonlinear residual problem. For the case where we are lacking the local convexity, we propose an appropriate convexification by quadratic perturbations. Eventually we are able to show convergence of this modified procedure to at least a very good approximation of stationary points of the original problem. In order to illustrate the theoretical results we conclude the paper with several numerical experiments. We first compare IRLS with standard Matlab optimization functions for a simple and easily presentable example. Furthermore we numerically validate our theoretical results in the more complicated framework of phase retrieval problems, which are our main motivation. Finally we examine the recovery capability of the algorithm in the context of data corrupted by impulsive noise where the sparsification of the residual is desired. 
BibTeX:
@article{S16,
author = {Sigl, Juliane},
title = {Nonlinear residual minimization by iteratively reweighted least squares},
journal = {Computational Optimization and Applications},
year = {2016},
volume = {64},
number = {3},
pages = {755792},
doi = {10.1007/s105890169829x}
}

J.A. Carrillo, Y.P. Choi and E. Zatorska. On the pressureless damped EulerPoisson equations with quadratic confinement: Critical thresholds and largetime behavior, Math. Mod. Meth. Appl. Sci., 26(12): 23112340, 2016.
[BibTeX] [arXiv]

BibTeX:
@article{CCZ16,
author = {Carrillo, José A. and Choi, YoungPil and Zatorska, Ewelina},
title = {On the pressureless damped EulerPoisson equations with quadratic confinement: Critical thresholds and largetime behavior},
journal = {Math. Mod. Meth. Appl. Sci.},
year = {2016},
volume = {26},
number = {12},
pages = {23112340},
url = {http://arxiv.org/abs/1604.05229},
doi = {10.1142/S0218202516500548}
}

Y.P. Choi. Global classical solutions and largetime behavior of the twophase fluid model, SIAM J. Math. Anal., 48(5):30903122, 2016.
[BibTeX] [arXiv]

BibTeX:
@article{CYP16_2,
author = {Choi, Y.P.},
title = {Global classical solutions and largetime behavior of the twophase fluid model},
journal = {SIAM J. Math. Anal.},
year = {2016},
volume = {48},
number = {5},
pages = {30903122},
url = {http://arxiv.org/pdf/1607.00177v1.pdf}
doi = {10.1137/15M1037196}
}

F. Krahmer and R. Ward. A unified framework for linear dimensionality reduction in L1, Results in Mathematics, 70(1):209231, 2016.
[BibTeX] [arXiv]

BibTeX:
@article{KW14,
author = {Krahmer, Felix and Ward, Rachel},
title = {A unified framework for linear dimensionality reduction in L1},
journal = {Results in Mathematics},
year = {2016},
volume = {70},
number = {1},
pages = {209231},
url = {http://arxiv.org/abs/1405.1332v5},
doi = {10.1007/s000250150475x}
}

M. Fornasier, S. Peter, H. Rauhut and S. Worm. Conjugate gradient acceleration of iteratively reweighted least squares methods, Computational Optimization and Applications, 65(1):205259, 2016.
[Abstract] [BibTeX] [arXiv] [.pdf]

Abstract Iteratively reweighted least squares (IRLS) is a method for solving minimization problems involving nonquadratic cost functions, perhaps nonconvex and nonsmooth, which however can be described as the infimum over a family of quadratic functions. This transformation suggests an algorithmic scheme that solves a sequence of quadratic problems to be tackled efficiently by tools of numerical linear algebra. Its general scope and its usually simple implementation, transforming the initial nonconvex and nonsmooth minimization problem into a more familiar and easily solvable quadratic optimization problem, make it a versatile algorithm. However, despite its simplicity, versatility, and elegant analysis, the complexity of IRLS strongly depends on the way the solution of the successive quadratic optimizations is addressed. For the important special case of compressed sensing and sparse recovery problems in signal processing, we investigate theoretically and numerically how accurately one needs to solve the quadratic problems by means of the conjugate gradient (CG) method in each iteration in order to guarantee convergence. The use of the CG method may significantly speedup the numerical solution of the quadratic subproblems, in particular, when fast matrixvector multiplication (exploiting for instance the FFT) is available for the matrix involved. In addition, we study convergence rates. Our modified IRLS method outperforms state of the art first order methods such as Iterative Hard Thresholding (IHT) or Fast Iterative SoftThresholding Algorithm (FISTA) in many situations, especially in large dimensions. Moreover, IRLS is often able to recover sparse vectors from fewer measurements than required for IHT and FISTA. 
BibTeX:
@article{Fornasier2016,
author = {Fornasier, Massimo and Peter, Steffen and Rauhut, Holger and Worm, Stephan},
title = {Conjugate gradient acceleration of iteratively reweighted least squares methods},
journal = {Computational Optimization and Applications},
year = {2016},
volume = {65},
number = {1},
pages = {205259},
url = {http://arxiv.org/abs/1509.04063},
doi = {10.1007/s1058901698398}
}

M. Fornasier and J.C. Hütter. Consistency of Probability Measure Quantization by Means of Power RepulsionAttraction Potentials, J. Fourier Anal. Appl., 22(3):694749, 2016.
[Abstract] [BibTeX] [.pdf]

Abstract This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The proof of consistency is based on the construction of a target energy functional whose unique minimizer is actually the given probability measure ω to be quantized. Then we show that the discrete functionals, defining the discrete quantizers as their minimizers, actually Γconverge to the target energy with respect to the narrow topology on the space of probability measures. A key ingredient is the reformulation of the target functional by means of a Fourier representation, which extends the characterization of conditionally positive semidefinite functions from points in generic position to probability measures. As a byproduct of the Fourier representation, we also obtain compactness of sublevels of the target energy in terms of uniform moment bounds, which already found applications in the asymptotic analysis of corresponding gradient flows. To model situations where the given probability is affected by noise, we further consider a modified energy, with the addition of a regularizing total variation term and we investigate again its point mass approximations in terms of Γconvergence. We show that such a discrete measure representation of the total variation can be interpreted as an additional nonlinear potential, repulsive at a short range, attractive at a medium range, and at a long range not having effect, promoting a uniform distribution of the point masses. 
BibTeX:
@article{FH15,
author = {Fornasier, Massimo and Hütter, JanChristian},
title = {Consistency of Probability Measure Quantization by Means of Power RepulsionAttraction Potentials},
journal = {J. Fourier Anal. Appl.},
year = {2016},
volume = {22},
number = {3},
pages = {694749},
doi = {10.1007/s000410159432z}
}

Y.P. Choi. Largetime behavior for the Vlasov/compressible NavierStokes equations, J. Math. Phys., 57(7):071501, 2016.
[BibTeX] [arXiv]

BibTeX:
@article{CYP16,
author = {Y.P. Choi},
title = {Largetime behavior for the Vlasov/compressible NavierStokes equations},
journal = {J. Math. Phys.},
year = {2016},
volume = {57},
number = {7},
pages = {071501},
url = {http://arxiv.org/pdf/1606.01007.pdf},
doi = {10.1063/1.4955026}
}

Y.P. Choi. Global classical solutions of the VlasovFokkerPlanck equation with local alignment forces, Nonlinearity, 29(7):18871916, 2016.
[BibTeX] [arXiv]

BibTeX:
@article{C16,
author = {Y.P. Choi},
title = {Global classical solutions of the VlasovFokkerPlanck equation with local alignment forces},
journal = {Nonlinearity},
year = {2016},
volume = {29},
number = {7},
pages = {18871916},
url = {http://iopscience.iop.org/article/10.1088/09517715/29/7/1887},
doi = {10.1088/09517715/29/7/1887}
}

Y.P. Choi and B. Kwon. The Cauchy problem for the pressureless Euler/isentropic NavierStokes equations, Journal of Differential Equations, 261(1):654711, 2016.
[BibTeX] [arXiv]

BibTeX:
@article{CK16,
author = {Y.P. Choi and B. Kwon},
title = {The Cauchy problem for the pressureless Euler/isentropic NavierStokes equations},
journal = {Journal of Differential Equations},
year = {2016},
volume = {261},
number = {1},
pages = {654711},
url = {http://arxiv.org/pdf/1604.04886.pdf},
doi = {10.1016/j.jde.2016.03.026}
}

K. Hahn, P.R. Massopust and S. Prigarin. A new method to measure complexity in binary or weighted networks and applications to functional connectivity in the human brain, BMC Bioinformatics, 17(1):118, 2016.
[Abstract] [BibTeX]

Abstract Networks or graphs play an important role in the biological sciences. Protein interaction networks and metabolic networks support the understanding of basic cellular mechanisms. In the human brain, networks of functional or structural connectivity model the informationflow between cortex regions. In this context, measures of network properties are needed. We propose a new measure, Ndim, estimating the complexity of arbitrary networks. This measure is based on a fractal dimension, which is similar to recently introduced boxcovering dimensions. However, boxcovering dimensions are only applicable to fractal networks. The construction of these networkdimensions relies on concepts proposed to measure fractality or complexity of irregular sets in ℝ n $backslashmathbb R\^n\$ . 
BibTeX:
@article{Hahn2016,
author = {Hahn, Klaus and Massopust, Peter R. and Prigarin, Sergei},
title = {A new method to measure complexity in binary or weighted networks and applications to functional connectivity in the human brain},
journal = {BMC Bioinformatics},
year = {2016},
volume = {17},
number = {1},
pages = {118},
doi = {10.1186/s1285901609339}
}

A. Israel, F. Krahmer and R. Ward. An arithmeticgeometric mean inequality for products of three matrices, Linear Algebra and its Applications, 488:112, 2016.
[BibTeX] [arXiv]

BibTeX:
@article{IKW14,
author = {Israel, Arie and Krahmer, Felix and Ward, Rachel},
title = {An arithmeticgeometric mean inequality for products of three matrices},
journal = {Linear Algebra and its Applications},
year = {2016},
volume = {488},
pages = {112},
url = {http://arxiv.org/abs/1411.0333},
doi = {10.1016/j.laa.2015.09.013}
}

S. Dahlke, L. Diening, C. Hartmann, B. Scharf and M. Weimar. Besov regularity of solutions to the pPoisson equation, Nonlinear Anal., 130:298329, 2016.
[BibTeX] [.pdf]

BibTeX:
@article{MR3424623,
author = {Dahlke, Stephan and Diening, Lars and Hartmann, Christoph and Scharf, Benjamin and Weimar, Markus},
title = {Besov regularity of solutions to the pPoisson equation},
journal = {Nonlinear Anal.},
year = {2016},
volume = {130},
pages = {298329},
doi = {10.1016/j.na.2015.10.015}
}

B. Piccoli, N. Pouradier Duteil and B. Scharf. Optimal control of a collective migration model, Math. Models Methods Appl. Sci., 26(2):383417, 2016.
[BibTeX] [arXiv]

BibTeX:
@article{MR3426205,
author = {Piccoli, Benedetto and Pouradier Duteil, Nastassia and Scharf, Benjamin},
title = {Optimal control of a collective migration model},
journal = {Math. Models Methods Appl. Sci.},
year = {2016},
volume = {26},
number = {2},
pages = {383417},
url = {http://arxiv.org/abs/1503.05168},
doi = {10.1142/S0218202516400066}
}

G. Albi, M. Artina, M. Fornasier and P.A. Markowich. Biological transportation networks: modeling and simulation, Anal. Appl. (Singap.), 14(1):185206, 2016.
[BibTeX]

BibTeX:
@article{MR3438650,
author = {Albi, Giacomo and Artina, Marco and Fornasier, Massimo and Markowich, Peter A.},
title = {Biological transportation networks: modeling and simulation},
journal = {Anal. Appl. (Singap.)},
year = {2016},
volume = {14},
number = {1},
pages = {185206},
doi = {10.1142/S0219530515400059}
}

M. Bongini, A. Ciabattoni and F. Montagna. Proof search and CoNP completeness for manyvalued logics, Fuzzy Sets and Systems, 292:130149, 2016.
[BibTeX] [.pdf]

BibTeX:
@article{MR3471212,
author = {Bongini, Mattia and Ciabattoni, Agata and Montagna, Franco},
title = {Proof search and CoNP completeness for manyvalued logics},
journal = {Fuzzy Sets and Systems},
year = {2016},
volume = {292},
pages = {130149},
doi = {10.1016/j.fss.2015.02.016}
}

P.R. Massopust. On local fractal functions in Besov and TriebelLizorkin spaces., J. Math. Anal. Appl., 436(1):393407, Elsevier, San Diego, CA, 2016.
[BibTeX]

BibTeX:
@article{zbMATH06536912,
author = {Peter R. Massopust},
title = {On local fractal functions in Besov and TriebelLizorkin spaces.},
journal = {J. Math. Anal. Appl.},
publisher = {Elsevier, San Diego, CA},
year = {2016},
volume = {436},
number = {1},
pages = {393407},
doi = {10.1016/j.jmaa.2015.12.019}
}

2015  M. Caponigro, M. Fornasier, B. Piccoli and E. Trélat. Sparse stabilization and control of alignment models, Mathematical Models and Methods in Applied Sciences, 25(03):521564, 2015.
[BibTeX] [.pdf]

BibTeX:
@article{CFPT15,
author = {Caponigro, Marco and Fornasier, Massimo and Piccoli, Benedetto and Trélat, Emmanuel},
title = {Sparse stabilization and control of alignment models},
journal = {Mathematical Models and Methods in Applied Sciences},
year = {2015},
volume = {25},
number = {03},
pages = {521564},
doi = {10.1142/S0218202515400059}
}

M. Iwen and F. Krahmer. Fast Subspace Approximation via Greedy LeastSquares, Constr. Approx., 42(2):281301, 2015.
[BibTeX] [.pdf]

BibTeX:
@article{IK13,
author = {Iwen, M. and Krahmer, F.},
title = {Fast Subspace Approximation via Greedy LeastSquares},
journal = {Constr. Approx.},
year = {2015},
volume = {42},
number = {2},
pages = {281301},
doi = {10.1007/s003650149273z}
}

F. Krahmer, D. Needell and R. Ward. Compressive Sensing with Redundant Dictionaries and Structured Measurements, SIAM J. Math. Anal., 47(6):46064629, 2015.
[BibTeX] [arXiv]

BibTeX:
@article{KNW15,
author = {Krahmer, Felix and Needell, Deanna and Ward, Rachel},
title = {Compressive Sensing with Redundant Dictionaries and Structured Measurements},
journal = {SIAM J. Math. Anal.},
year = {2015},
volume = {47},
number = {6},
pages = {46064629},
url = {http://arxiv.org/abs/1501.03208},
doi = {10.1137/151005245}
}

M. Hansen. Nonlinear approximation rates and Besov regularity for elliptic PDEs on polyhedral domains, Found. Comput. Math., 15(2):561589, 2015.
[BibTeX] [.pdf]

BibTeX:
@article{MR3320933,
author = {Hansen, Markus},
title = {Nonlinear approximation rates and Besov regularity for elliptic PDEs on polyhedral domains},
journal = {Found. Comput. Math.},
year = {2015},
volume = {15},
number = {2},
pages = {561589},
doi = {10.1007/s102080149224x}
}

C.K. Chui, F. Filbir and H.N. Mhaskar. Representation of functions on big data: graphs and trees, Appl. Comput. Harmon. Anal., 38(3):489509, 2015.
[BibTeX]

BibTeX:
@article{MR3323114,
author = {Chui, C. K. and Filbir, F. and Mhaskar, H. N.},
title = {Representation of functions on big data: graphs and trees},
journal = {Appl. Comput. Harmon. Anal.},
year = {2015},
volume = {38},
number = {3},
pages = {489509},
doi = {10.1016/j.acha.2014.06.006}
}

G. Albi, M. Herty and L. Pareschi. Kinetic description of optimal control problems and applications to opinion consensus, Commun. Math. Sci., 13(6):14071429, 2015.
[BibTeX] [arXiv]

BibTeX:
@article{MR3351435,
author = {Albi, Giacomo and Herty, Michael and Pareschi, Lorenzo},
title = {Kinetic description of optimal control problems and applications to opinion consensus},
journal = {Commun. Math. Sci.},
year = {2015},
volume = {13},
number = {6},
pages = {14071429},
url = {http://arxiv.org/abs/1401.7798},
doi = {10.4310/CMS.2015.v13.n6.a3}
}

G. Albi, L. Pareschi and M. Zanella. Uncertainty quantification in control problems for flocking models, Math. Probl. Eng.:Art. ID 850124, 14, 2015.
[BibTeX] [.pdf]

BibTeX:
@article{MR3356715,
author = {Albi, Giacomo and Pareschi, Lorenzo and Zanella, Mattia},
title = {Uncertainty quantification in control problems for flocking models},
journal = {Math. Probl. Eng.},
year = {2015},
pages = {Art. ID 850124, 14},
doi = {10.1155/2015/850124}
}

M. Artina, M. Fornasier, S. Micheletti and S. Perotto. Anisotropic mesh adaptation for crack detection in brittle materials, SIAM J. Sci. Comput., 37(4):B633B659, 2015.
[BibTeX] [.pdf]

BibTeX:
@article{MR3376787,
author = {Artina, Marco and Fornasier, Massimo and Micheletti, Stefano and Perotto, Simona},
title = {Anisotropic mesh adaptation for crack detection in brittle materials},
journal = {SIAM J. Sci. Comput.},
year = {2015},
volume = {37},
number = {4},
pages = {B633B659},
doi = {10.1137/140970495}
}

S. Dahlke, M. Fornasier, U. Friedrich and T. Raasch. Multilevel preconditioning for sparse optimization of functionals with nonconvex fidelity terms, J. Inverse IllPosed Probl., 23(4):393414, 2015.
[BibTeX] [.pdf]

BibTeX:
@article{MR3377417,
author = {Dahlke, Stephan and Fornasier, Massimo and Friedrich, Ulrich and Raasch, Thorsten},
title = {Multilevel preconditioning for sparse optimization of functionals with nonconvex fidelity terms},
journal = {J. Inverse IllPosed Probl.},
year = {2015},
volume = {23},
number = {4},
pages = {393414},
doi = {10.1515/jiip20140031}
}

M. Bongini, M. Fornasier and D. Kalise. (Un)conditional consensus emergence under perturbed and decentralized feedback controls, Discrete Contin. Dyn. Syst., 35(9):40714094, 2015.
[BibTeX] [.pdf]

BibTeX:
@article{MR3392618,
author = {Bongini, Mattia and Fornasier, Massimo and Kalise, Dante},
title = {(Un)conditional consensus emergence under perturbed and decentralized feedback controls},
journal = {Discrete Contin. Dyn. Syst.},
year = {2015},
volume = {35},
number = {9},
pages = {40714094},
doi = {10.3934/dcds.2015.35.4071}
}

S. Peter, M. Artina and M. Fornasier. Damping noisefolding and enhanced support recovery in compressed sensing, IEEE Trans. Signal Process., 63(22):59906002, 2015.
[BibTeX] [.pdf]

BibTeX:
@article{MR3411372,
author = {Peter, Steffen and Artina, Marco and Fornasier, Massimo},
title = {Damping noisefolding and enhanced support recovery in compressed sensing},
journal = {IEEE Trans. Signal Process.},
year = {2015},
volume = {63},
number = {22},
pages = {59906002},
doi = {10.1109/TSP.2015.2461521}
}

M. Bongini, M. Fornasier, O. Junge and B. Scharf. Sparse control of alignment models in high dimension, Netw. Heterog. Media, 10(3):647697, 2015.
[BibTeX] [.pdf]

BibTeX:
@article{MR3431286,
author = {Bongini, Mattia and Fornasier, Massimo and Junge, Oliver and Scharf, Benjamin},
title = {Sparse control of alignment models in high dimension},
journal = {Netw. Heterog. Media},
year = {2015},
volume = {10},
number = {3},
pages = {647697},
doi = {10.3934/nhm.2015.10.647}
}

M. Sandbichler, F. Krahmer, T. Berer, P. Burgholzer and M. Haltmeier. A Novel Compressed Sensing Scheme for Photoacoustic Tomography, SIAM J. Appl. Math., 75(6):24752494, 2015.
[BibTeX] [arXiv]

BibTeX:
@article{SKBBH15,
author = {Sandbichler, M. and Krahmer, F. and Berer, T. and Burgholzer, P. and Haltmeier, M.},
title = {A Novel Compressed Sensing Scheme for Photoacoustic Tomography},
journal = {SIAM J. Appl. Math.},
year = {2015},
volume = {75},
number = {6},
pages = {24752494},
url = {http://arxiv.org/abs/1501.04305},
doi = {10.1137/141001408}
}

2014  J. Feng and F. Krahmer. An RIP approach to SigmaDelta quantization for compressed sensing, IEEE Signal Process. Lett., 21(11):13511355, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{FK14,
author = {Feng, J. and Krahmer, F},
title = {An RIP approach to SigmaDelta quantization for compressed sensing},
journal = {IEEE Signal Process. Lett.},
year = {2014},
volume = {21},
number = {11},
pages = {13511355},
doi = {10.1109/LSP.2014.2336700}
}

D. Gross, F. Krahmer and R. Küng. A Partial Derandomization of PhaseLift using Spherical Designs, J Fourier Anal. Appl., 21(2):229266, 2014.
[BibTeX] [arXiv]

BibTeX:
@article{GKK13,
author = {Gross, D. and Krahmer, F. and Küng, R.},
title = {A Partial Derandomization of !PhaseLift using Spherical Designs},
journal = {J Fourier Anal. Appl.},
year = {2014},
volume = {21},
number = {2},
pages = {229266},
url = {http://arxiv.org/abs/1310.2267},
doi = {10.1007/s0004101493612}
}

F. Krahmer, G. Kutyniok and J. Lemvig. Sparse Matrices in Frame Theory, Computational Statistics, 29:547568, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{KKL12b,
author = {Krahmer, F. and Kutyniok, G. and Lemvig, J.},
title = {Sparse Matrices in Frame Theory},
journal = {Computational Statistics},
year = {2014},
volume = {29},
pages = {547568},
doi = {10.1007/s0018001304461}
}

F.. Krahmer, S.. Mendelson and H.. Rauhut. Suprema of Chaos Processes and the Restricted Isometry Property, Comm. Pure Appl. Math., 67(11):18771904, 2014.
[BibTeX] [arXiv]

BibTeX:
@article{KMR12,
author = {Krahmer, F. and Mendelson, S. and Rauhut, H.},
title = {Suprema of Chaos Processes and the Restricted Isometry Property},
journal = {Comm. Pure Appl. Math.},
year = {2014},
volume = {67},
number = {11},
pages = {18771904},
url = {http://arxiv.org/abs/1207.0235},
doi = {10.1002/cpa.21504}
}

F.. Krahmer and G.. Pfander. Local sampling and approximation of operators with bandlimited KohnNirenberg symbols, Constr. Approx., 39(3):541572, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{KP13,
author = {Krahmer, F. and Pfander, G.},
title = {Local sampling and approximation of operators with bandlimited KohnNirenberg symbols},
journal = {Constr. Approx.},
year = {2014},
volume = {39},
number = {3},
pages = {541572},
doi = {10.1007/s0036501492284}
}

F.. Krahmer and H.. Rauhut. Structured random measurements in signal processing, GAMMMitteilungen, 37(2):217238, 2014.
[BibTeX] [.pdf]

BibTeX:
@inproceedings{KR14,
author = {Krahmer, F. and Rauhut, H.},
title = {Structured random measurements in signal processing},
journal = {GAMMMitteilungen},
year = {2014},
volume = {37},
number = {2},
pages = {217238},
doi = {10.1002/gamm.201410010}
}

F. Krahmer, R. Saab and Ö. Yilmaz. SigmaDelta quantization of subGaussian frame expansions and its application to compressed sensing, Inform. Inference, 3(1):4058, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{KSY13,
author = {Krahmer, F. and Saab, R. and Yilmaz, Ö.},
title = {SigmaDelta quantization of subGaussian frame expansions and its application to compressed sensing},
journal = {Inform. Inference},
year = {2014},
volume = {3},
number = {1},
pages = {4058},
doi = {10.1093/imaiai/iat007}
}

F. Krahmer and R. Ward. Stable and robust sampling strategies for compressive imaging, IEEE Trans. Image Proc., 23(2):612622, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{KW13,
author = {F. Krahmer and R. Ward},
title = {Stable and robust sampling strategies for compressive imaging},
journal = {IEEE Trans. Image Proc.},
year = {2014},
volume = {23},
number = {2},
pages = {612622},
doi = {10.1109/TIP.2013.2288004}
}

B. Scharf. Wavelet decomposition techniques and Hardy inequalities for function spaces on cubes, J. Approx. Theory, 178:4163, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{MR3145754,
author = {Scharf, B.},
title = {Wavelet decomposition techniques and Hardy inequalities for function spaces on cubes},
journal = {J. Approx. Theory},
year = {2014},
volume = {178},
pages = {4163},
doi = {10.1016/j.jat.2013.11.006}
}

M. Bongini and M. Fornasier. Sparse stabilization of dynamical systems driven by attraction and avoidance forces, Netw. Heterog. Media, 9(1):131, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{MR3195343,
author = {Bongini, Mattia and Fornasier, Massimo},
title = {Sparse stabilization of dynamical systems driven by attraction and avoidance forces},
journal = {Netw. Heterog. Media},
year = {2014},
volume = {9},
number = {1},
pages = {131},
doi = {10.3934/nhm.2014.9.1}
}

M. Ehler, M. Fornasier and J. Sigl. Quasilinear compressed sensing, Multiscale Model. Simul., 12(2):725754, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{MR3213786,
author = {Ehler, Martin and Fornasier, Massimo and Sigl, Juliane},
title = {Quasilinear compressed sensing},
journal = {Multiscale Model. Simul.},
year = {2014},
volume = {12},
number = {2},
pages = {725754},
doi = {10.1137/130929928}
}

G. Albi, D. Balagué, J.A. Carrillo and J. von Brecht. Stability analysis of flock and mill rings for second order models in swarming, SIAM J. Appl. Math., 74(3):794818, 2014.
[BibTeX] [arXiv]

BibTeX:
@article{MR3215070,
author = {Albi, G. and Balagué, D. and Carrillo, J. A. and von Brecht, J.},
title = {Stability analysis of flock and mill rings for second order models in swarming},
journal = {SIAM J. Appl. Math.},
year = {2014},
volume = {74},
number = {3},
pages = {794818},
url = {http://arxiv.org/abs/1304.5459},
doi = {10.1137/13091779X}
}

M. Ehler and F. Filbir. varepsiloncoverings of HölderZygmund type spaces on datadefined manifolds, Abstr. Appl. Anal.:Art. ID 402918, 6, 2014.
[BibTeX]

BibTeX:
@article{MR3226192,
author = {Ehler, Martin and Filbir, Frank},
title = {varepsiloncoverings of HölderZygmund type spaces on datadefined manifolds},
journal = {Abstr. Appl. Anal.},
year = {2014},
pages = {Art. ID 402918, 6},
doi = {10.1155/2014/402918}
}

M. Fornasier, V. Naumova and S.V. Pereverzyev. Parameter choice strategies for multipenalty regularization, SIAM J. Numer. Anal., 52(4):17701794, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{MR3239768,
author = {Fornasier, Massimo and Naumova, Valeriya and Pereverzyev, Sergei V.},
title = {Parameter choice strategies for multipenalty regularization},
journal = {SIAM J. Numer. Anal.},
year = {2014},
volume = {52},
number = {4},
pages = {17701794},
doi = {10.1137/130930248}
}

M. Fornasier and F. Solombrino. Meanfield optimal control, ESAIM Control Optim. Calc. Var., 20(4):11231152, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{MR3264236,
author = {Fornasier, Massimo and Solombrino, Francesco},
title = {Meanfield optimal control},
journal = {ESAIM Control Optim. Calc. Var.},
year = {2014},
volume = {20},
number = {4},
pages = {11231152},
doi = {10.1051/cocv/2014009}
}

G. Albi, M. Herty, C. Jörres and L. Pareschi. Asymptotic preserving timediscretization of optimal control problems for the GoldsteinTaylor model, Numer. Methods Partial Differential Equations, 30(6):17701784, 2014.
[BibTeX] [arXiv]

BibTeX:
@article{MR3267352,
author = {Albi, Giacomo and Herty, Michael and Jörres, Christian and Pareschi, Lorenzo},
title = {Asymptotic preserving timediscretization of optimal control problems for the GoldsteinTaylor model},
journal = {Numer. Methods Partial Differential Equations},
year = {2014},
volume = {30},
number = {6},
pages = {17701784},
url = {http://arxiv.org/pdf/1307.8303v2.pdf},
doi = {10.1002/num.21877}
}

M. Fornasier, B. Piccoli and F. Rossi. Meanfield sparse optimal control, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 372(2028):20130400, 21, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{MR3268059,
author = {Fornasier, Massimo and Piccoli, Benedetto and Rossi, Francesco},
title = {Meanfield sparse optimal control},
journal = {Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.},
year = {2014},
volume = {372},
number = {2028},
pages = {20130400, 21},
doi = {10.1098/rsta.2013.0400}
}

G. Albi, L. Pareschi and M. Zanella. Boltzmanntype control of opinion consensus through leaders, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 372(2028):20140138, 18, 2014.
[BibTeX] [arXiv]

BibTeX:
@article{MR3268062,
author = {Albi, G. and Pareschi, L. and Zanella, M.},
title = {Boltzmanntype control of opinion consensus through leaders},
journal = {Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.},
year = {2014},
volume = {372},
number = {2028},
pages = {20140138, 18},
url = {https://arxiv.org/abs/1405.0736},
doi = {10.1098/rsta.2014.0138}
}

F. Filbir, S. Kunis and R. Seyfried. Effective discretization of direct reconstruction schemes for photoacoustic imaging in spherical geometries, SIAM J. Numer. Anal., 52(6):27222742, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{MR3277220,
author = {Filbir, Frank and Kunis, Stefan and Seyfried, Ruben},
title = {Effective discretization of direct reconstruction schemes for photoacoustic imaging in spherical geometries},
journal = {SIAM J. Numer. Anal.},
year = {2014},
volume = {52},
number = {6},
pages = {27222742},
doi = {10.1137/130944898}
}

M. Di Francesco, M. Fornasier, J.C. Hütter and D. Matthes. Asymptotic behavior of gradient flows driven by nonlocal power repulsion and attraction potentials in one dimension, SIAM J. Math. Anal., 46(6):38143837, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{MR3280100,
author = {Di Francesco, Marco and Fornasier, Massimo and Hütter, JanChristian and Matthes, Daniel},
title = {Asymptotic behavior of gradient flows driven by nonlocal power repulsion and attraction potentials in one dimension},
journal = {SIAM J. Math. Anal.},
year = {2014},
volume = {46},
number = {6},
pages = {38143837},
doi = {10.1137/140951497}
}

V. Naumova and S. Peter. Minimization of multipenalty functionals by alternating iterative thresholding and optimal parameter choices, Inverse Problems, 30(12):125003, 34, 2014.
[BibTeX] [.pdf]

BibTeX:
@article{MR3291117,
author = {Naumova, Valeriya and Peter, Steffen},
title = {Minimization of multipenalty functionals by alternating iterative thresholding and optimal parameter choices},
journal = {Inverse Problems},
year = {2014},
volume = {30},
number = {12},
pages = {125003, 34},
doi = {10.1088/02665611/30/12/125003}
}

2013  F. Krahmer, G. Kutyniok and J. Lemvig. Sparsity and spectral properties of dual frames, Linear Algebra and its Applications , 439(4):982  998, 2013.
[BibTeX] [.pdf]

BibTeX:
@article{KKL13,
author = {Krahmer, F. and Kutyniok, G. and Lemvig, J.},
title = {Sparsity and spectral properties of dual frames},
journal = {Linear Algebra and its Applications },
year = {2013},
volume = {439},
number = {4},
pages = {982  998},
doi = {10.1016/j.laa.2012.10.016}
}

M. Ansorg, F. Filbir, W.R. Madych and R. Seyfried. Summability kernels for circular and spherical mean data, Inverse Problems, 29(1):015002, 13, 2013.
[BibTeX]

BibTeX:
@article{MR3003009,
author = {Ansorg, Marcus and Filbir, Frank and Madych, W. R. and Seyfried, Ruben},
title = {Summability kernels for circular and spherical mean data},
journal = {Inverse Problems},
year = {2013},
volume = {29},
number = {1},
pages = {015002, 13},
doi = {10.1088/02665611/29/1/015002}
}

M. Fornasier, R. March and F. Solombrino. Existence of minimizers of the MumfordShah functional with singular operators and unbounded data, Ann. Mat. Pura Appl. (4), 192(3):361391, 2013.
[BibTeX] [.pdf]

BibTeX:
@article{MR3061104,
author = {Fornasier, Massimo and March, Riccardo and Solombrino, Francesco},
title = {Existence of minimizers of the MumfordShah functional with singular operators and unbounded data},
journal = {Ann. Mat. Pura Appl. (4)},
year = {2013},
volume = {192},
number = {3},
pages = {361391},
doi = {10.1007/s1023101102288}
}

M. Artina, M. Fornasier and F. Solombrino. Linearly constrained nonsmooth and nonconvex minimization, SIAM J. Optim., 23(3):19041937, 2013.
[BibTeX] [.pdf]

BibTeX:
@article{MR3106492,
author = {Artina, Marco and Fornasier, Massimo and Solombrino, Francesco},
title = {Linearly constrained nonsmooth and nonconvex minimization},
journal = {SIAM J. Optim.},
year = {2013},
volume = {23},
number = {3},
pages = {19041937},
doi = {10.1137/120869079}
}

M. Caponigro, M. Fornasier, B. Piccoli and E. Trélat. Sparse stabilization and optimal control of the CuckerSmale model, Math. Control Relat. Fields, 3(4):447466, 2013.
[BibTeX] [.pdf]

BibTeX:
@article{MR3110059,
author = {Caponigro, Marco and Fornasier, Massimo and Piccoli, Benedetto and Trélat, Emmanuel},
title = {Sparse stabilization and optimal control of the CuckerSmale model},
journal = {Math. Control Relat. Fields},
year = {2013},
volume = {3},
number = {4},
pages = {447466},
doi = {10.3934/mcrf.2013.3.447}
}

M. Fornasier, J. Haškovec and G. Steidl. Consistency of variational continuousdomain quantization via kinetic theory, Appl. Anal., 92(6):12831298, 2013.
[BibTeX] [.pdf]

BibTeX:
@article{MR3197935,
author = {Fornasier, Massimo and Haškovec, Jan and Steidl, Gabriele},
title = {Consistency of variational continuousdomain quantization via kinetic theory},
journal = {Appl. Anal.},
year = {2013},
volume = {92},
number = {6},
pages = {12831298},
doi = {10.1080/00036811.2012.671299}
}

2012  M. Burr and F. Krahmer. SqFreeEVAL: An (almost) optimal realroot isolation algorithm, Journal of Symbolic Computation, 47(2):153166, 2012.
[BibTeX] [.pdf]

BibTeX:
@article{BK11,
author = {Burr, M. and Krahmer, F.},
title = {SqFreeEVAL: An (almost) optimal realroot isolation algorithm},
journal = {Journal of Symbolic Computation},
year = {2012},
volume = {47},
number = {2},
pages = {153166},
doi = {10.1016/j.jsc.2011.08.022}
}

F. Krahmer, R. Saab and R. Ward. Rootexponential accuracy for coarse quantization of finite frame expansions, IEEE J. Inf. Theo., 58(2):10691079, 2012.
[BibTeX] [.pdf]

BibTeX:
@article{KSW12,
author = {Krahmer, F. and Saab, R. and Ward, R.},
title = {Rootexponential accuracy for coarse quantization of finite frame expansions},
journal = {IEEE J. Inf. Theo.},
year = {2012},
volume = {58},
number = {2},
pages = {10691079},
doi = {10.1109/TIT.2011.2168942}
}

F. Krahmer and R. Ward. Lower bounds for the error decay incurred by coarse quantization schemes, Appl. Comput. Harmonic Anal., 32(1):131138, 2012.
[BibTeX] [.pdf]

BibTeX:
@article{KW12,
author = {Krahmer, F. and Ward, R.},
title = {Lower bounds for the error decay incurred by coarse quantization schemes},
journal = {Appl. Comput. Harmonic Anal.},
year = {2012},
volume = {32},
number = {1},
pages = {131138},
doi = {10.1016/j.acha.2011.06.003}
}

S. Dahlke, M. Fornasier and T. Raasch. Multilevel preconditioning and adaptive sparse solution of inverse problems, Math. Comp., 81(277):419446, 2012.
[BibTeX] [.pdf]

BibTeX:
@article{MR2833502,
author = {Dahlke, Stephan and Fornasier, Massimo and Raasch, Thorsten},
title = {Multilevel preconditioning and adaptive sparse solution of inverse problems},
journal = {Math. Comp.},
year = {2012},
volume = {81},
number = {277},
pages = {419446},
doi = {10.1090/S00255718201102507X}
}

M. Fornasier, K. Schnass and J. Vybiral. Learning functions of few arbitrary linear parameters in high dimensions, Found. Comput. Math., 12(2):229262, 2012.
[BibTeX] [.pdf]

BibTeX:
@article{MR2898783,
author = {Fornasier, Massimo and Schnass, Karin and Vybiral, Jan},
title = {Learning functions of few arbitrary linear parameters in high dimensions},
journal = {Found. Comput. Math.},
year = {2012},
volume = {12},
number = {2},
pages = {229262},
doi = {10.1007/s102080129115y}
}

M. Ehler, F. Filbir and H.N. Mhaskar. Locally learning biomedical data using diffusion frames, J. Comput. Biol., 19(11):12511264, 2012.
[BibTeX]

BibTeX:
@article{MR2994881,
author = {Ehler, M. and Filbir, F. and Mhaskar, H. N.},
title = {Locally learning biomedical data using diffusion frames},
journal = {J. Comput. Biol.},
year = {2012},
volume = {19},
number = {11},
pages = {12511264},
doi = {10.1089/cmb.2012.0187}
}

M. Fornasier, Y. Kim, A. Langer and C.B. Schönlieb. Wavelet decomposition method for L_2/TVimage deblurring, SIAM J. Imaging Sci., 5(3):857885, 2012.
[BibTeX] [.pdf]

BibTeX:
@article{MR3022181,
author = {Fornasier, M. and Kim, Y. and Langer, A. and Schönlieb, C.B.},
title = {Wavelet decomposition method for L_2/TVimage deblurring},
journal = {SIAM J. Imaging Sci.},
year = {2012},
volume = {5},
number = {3},
pages = {857885},
doi = {10.1137/100819801}
}

2011  P. Casazza, A. Heinecke, F. Krahmer and G. Kutyniok. Optimally sparse frames, IEEE J. Inf. Theo., 57(11):72797287, 2011.
[BibTeX] [.pdf]

BibTeX:
@article{CHKK11,
author = {Casazza, P. and Heinecke, A. and Krahmer, F. and Kutyniok, G.},
title = {Optimally sparse frames},
journal = {IEEE J. Inf. Theo.},
year = {2011},
volume = {57},
number = {11},
pages = {72797287},
doi = {10.1109/TIT.2011.2160521}
}

P. Deift, C.S. Güntürk and F. Krahmer. An Optimal Family of Exponentially Accurate OneBit SigmaDelta Quantization Schemes, Comm. Pure Appl. Math., 64(7):883919, 2011.
[BibTeX] [.pdf]

BibTeX:
@article{DGK11,
author = {Percy Deift and C. Sinan Güntürk and Felix Krahmer},
title = {An Optimal Family of Exponentially Accurate OneBit SigmaDelta Quantization Schemes},
journal = {Comm. Pure Appl. Math.},
year = {2011},
volume = {64},
number = {7},
pages = {883919},
doi = {10.1002/cpa.20367}
}

F. Krahmer and R. Ward. New and improved JohnsonLindenstrauss embeddings via the Restricted Isometry Property, SIAM J. Math. Anal., 43(3):12691281, SIAM, 2011.
[BibTeX] [.pdf]

BibTeX:
@article{KW11,
author = {Krahmer, F. and Ward, R.},
title = {New and improved JohnsonLindenstrauss embeddings via the Restricted Isometry Property},
journal = {SIAM J. Math. Anal.},
publisher = {SIAM},
year = {2011},
volume = {43},
number = {3},
pages = {12691281},
doi = {10.1137/100810447}
}

M. Fornasier, J. Haskovec and G. Toscani. Fluid dynamic description of flocking via the PovznerBoltzmann equation, Phys. D, 240(1):2131, 2011.
[BibTeX] [.pdf]

BibTeX:
@article{MR2740099,
author = {Fornasier, Massimo and Haskovec, Jan and Toscani, Giuseppe},
title = {Fluid dynamic description of flocking via the PovznerBoltzmann equation},
journal = {Phys. D},
year = {2011},
volume = {240},
number = {1},
pages = {2131},
doi = {10.1016/j.physd.2010.08.003}
}

M. Fornasier, J. Haškovec and J. Vybral. Particle systems and kinetic equations modeling interacting agents in high dimension, Multiscale Model. Simul., 9(4):17271764, 2011.
[BibTeX] [.pdf]

BibTeX:
@article{MR2861256,
author = {Fornasier, M. and Haškovec, J. and Vybral, J.},
title = {Particle systems and kinetic equations modeling interacting agents in high dimension},
journal = {Multiscale Model. Simul.},
year = {2011},
volume = {9},
number = {4},
pages = {17271764},
doi = {10.1137/110830617}
}

M. Fornasier, H. Rauhut and R. Ward. Lowrank matrix recovery via iteratively reweighted least squares minimization, SIAM J. Optim., 21(4):16141640, 2011.
[BibTeX] [.pdf]

BibTeX:
@article{MR2869510,
author = {Fornasier, Massimo and Rauhut, Holger and Ward, Rachel},
title = {Lowrank matrix recovery via iteratively reweighted least squares minimization},
journal = {SIAM J. Optim.},
year = {2011},
volume = {21},
number = {4},
pages = {16141640},
doi = {10.1137/100811404}
}

2010  S. Dahlke, M. Fornasier and K. Gröchenig. Optimal adaptive computations in the Jaffard algebra and localized frames, J. Approx. Theory, 162(1):153185, 2010.
[BibTeX] [.pdf]

BibTeX:
@article{MR2565831,
author = {Dahlke, Stephan and Fornasier, Massimo and Gröchenig, Karlheinz},
title = {Optimal adaptive computations in the Jaffard algebra and localized frames},
journal = {J. Approx. Theory},
year = {2010},
volume = {162},
number = {1},
pages = {153185},
doi = {10.1016/j.jat.2009.04.001}
}

I. Daubechies, R. DeVore, M. Fornasier and C.S. Güntürk. Iteratively reweighted least squares minimization for sparse recovery, Comm. Pure Appl. Math., 63(1):138, 2010.
[BibTeX] [.pdf]

BibTeX:
@article{MR2588385,
author = {Daubechies, Ingrid and !DeVore, Ronald and Fornasier, Massimo and Güntürk, C. Sinan},
title = {Iteratively reweighted least squares minimization for sparse recovery},
journal = {Comm. Pure Appl. Math.},
year = {2010},
volume = {63},
number = {1},
pages = {138},
doi = {10.1002/cpa.20303}
}

J.A. Carrillo, M. Fornasier, J. Rosado and G. Toscani. Asymptotic flocking dynamics for the kinetic CuckerSmale model, SIAM J. Math. Anal., 42(1):218236, 2010.
[BibTeX] [.pdf]

BibTeX:
@article{MR2596552,
author = {Carrillo, J. A. and Fornasier, M. and Rosado, J. and Toscani, G.},
title = {Asymptotic flocking dynamics for the kinetic CuckerSmale model},
journal = {SIAM J. Math. Anal.},
year = {2010},
volume = {42},
number = {1},
pages = {218236},
doi = {10.1137/090757290}
}

M. Fornasier and R. Ward. Iterative thresholding meets freediscontinuity problems, Found. Comput. Math., 10(5):527567, 2010.
[BibTeX] [.pdf]

BibTeX:
@article{MR2673428,
author = {Fornasier, Massimo and Ward, Rachel},
title = {Iterative thresholding meets freediscontinuity problems},
journal = {Found. Comput. Math.},
year = {2010},
volume = {10},
number = {5},
pages = {527567},
doi = {10.1007/s1020801090713}
}

M. Fornasier, A. Langer and C.B. Schönlieb. A convergent overlapping domain decomposition method for total variation minimization, Numer. Math., 116(4):645685, 2010.
[BibTeX] [.pdf]

BibTeX:
@article{MR2721637,
author = {Fornasier, Massimo and Langer, Andreas and Schönlieb, CarolaBibiane},
title = {A convergent overlapping domain decomposition method for total variation minimization},
journal = {Numer. Math.},
year = {2010},
volume = {116},
number = {4},
pages = {645685},
doi = {10.1007/s0021101003147}
}

R. Duan, M. Fornasier and G. Toscani. A kinetic flocking model with diffusion, Comm. Math. Phys., 300(1):95145, 2010.
[BibTeX] [.pdf]

BibTeX:
@article{MR2725184,
author = {Duan, Renjun and Fornasier, Massimo and Toscani, Giuseppe},
title = {A kinetic flocking model with diffusion},
journal = {Comm. Math. Phys.},
year = {2010},
volume = {300},
number = {1},
pages = {95145},
doi = {10.1007/s002200101110z}
}

2009  M. Fornasier, R. Ramlau and G. Teschke. The application of joint sparsity and total variation minimization algorithms to a reallife art restoration problem, Adv. Comput. Math., 31(13):157184, 2009.
[BibTeX] [.pdf]

BibTeX:
@article{MR2511578,
author = {Fornasier, Massimo and Ramlau, Ronny and Teschke, Gerd},
title = {The application of joint sparsity and total variation minimization algorithms to a reallife art restoration problem},
journal = {Adv. Comput. Math.},
year = {2009},
volume = {31},
number = {13},
pages = {157184},
doi = {10.1007/s1044400891036}
}

M. Fornasier and C.B. Schönlieb. Subspace correction methods for total variation and l_1minimization, SIAM J. Numer. Anal., 47(5):33973428, 2009.
[BibTeX] [.pdf]

BibTeX:
@article{MR2551200,
author = {Fornasier, Massimo and Schönlieb, CarolaBibiane},
title = {Subspace correction methods for total variation and l_1minimization},
journal = {SIAM J. Numer. Anal.},
year = {2009},
volume = {47},
number = {5},
pages = {33973428},
doi = {10.1137/070710779}
}

S. Dahlke, M. Fornasier, M. Primbs, T. Raasch and M. Werner. Nonlinear and adaptive frame approximation schemes for elliptic PDEs: theory and numerical experiments, Numer. Methods Partial Differential Equations, 25(6):13661401, 2009.
[BibTeX] [.pdf]

BibTeX:
@article{MR2561555,
author = {Dahlke, Stephan and Fornasier, Massimo and Primbs, Miriam and Raasch, Thorsten and Werner, Manuel},
title = {Nonlinear and adaptive frame approximation schemes for elliptic PDEs: theory and numerical experiments},
journal = {Numer. Methods Partial Differential Equations},
year = {2009},
volume = {25},
number = {6},
pages = {13661401},
doi = {10.1002/num.20407}
}

2008  F. Krahmer, Gö.E. Pfander and P. Rashkov. Uncertainty in timefrequency representations on finite abelian groups and applications, Appl. Comput. Harmon. Anal., 25(2):209225, 2008.
[BibTeX] [.pdf]

BibTeX:
@article{KraPfaRa08,
author = {Krahmer, Felix and Pfander, Götz E. and Rashkov, Peter},
title = {Uncertainty in timefrequency representations on finite abelian groups and applications},
journal = {Appl. Comput. Harmon. Anal.},
year = {2008},
volume = {25},
number = {2},
pages = {209225},
doi = {10.1016/j.acha.2007.09.008}
}

M. Charina, C. Conti and M. Fornasier. Adaptive frame methods for nonlinear variational problems, Numer. Math., 109(1):4575, 2008.
[BibTeX] [.pdf]

BibTeX:
@article{MR2377612,
author = {Charina, Maria and Conti, Costanza and Fornasier, Massimo},
title = {Adaptive frame methods for nonlinear variational problems},
journal = {Numer. Math.},
year = {2008},
volume = {109},
number = {1},
pages = {4575},
doi = {10.1007/s0021100701275}
}

M. Fornasier and H. Rauhut. Recovery algorithms for vectorvalued data with joint sparsity constraints, SIAM J. Numer. Anal., 46(2):577613, 2008.
[BibTeX] [.pdf]

BibTeX:
@article{MR2383204,
author = {Fornasier, Massimo and Rauhut, Holger},
title = {Recovery algorithms for vectorvalued data with joint sparsity constraints},
journal = {SIAM J. Numer. Anal.},
year = {2008},
volume = {46},
number = {2},
pages = {577613},
doi = {10.1137/0606668909}
}

S. Dahlke, M. Fornasier, H. Rauhut, G. Steidl and G. Teschke. Generalized coorbit theory, Banach frames, and the relation to αmodulation spaces, Proc. Lond. Math. Soc. (3), 96(2):464506, 2008.
[BibTeX] [.pdf]

BibTeX:
@article{MR2396847,
author = {Dahlke, Stephan and Fornasier, Massimo and Rauhut, Holger and Steidl, Gabriele and Teschke, Gerd},
title = {Generalized coorbit theory, Banach frames, and the relation to αmodulation spaces},
journal = {Proc. Lond. Math. Soc. (3)},
year = {2008},
volume = {96},
number = {2},
pages = {464506},
doi = {10.1112/plms/pdm051}
}

M. Fornasier and H. Rauhut. Iterative thresholding algorithms, Appl. Comput. Harmon. Anal., 25(2):187208, 2008.
[BibTeX] [.pdf]

BibTeX:
@article{MR2436769,
author = {Fornasier, Massimo and Rauhut, Holger},
title = {Iterative thresholding algorithms},
journal = {Appl. Comput. Harmon. Anal.},
year = {2008},
volume = {25},
number = {2},
pages = {187208},
doi = {10.1016/j.acha.2007.10.005}
}

M. Fornasier and L. Gori. Sampling theorems on bounded domains, J. Comput. Appl. Math., 221(2):376385, 2008.
[BibTeX] [.pdf]

BibTeX:
@article{MR2457670,
author = {Fornasier, Massimo and Gori, Laura},
title = {Sampling theorems on bounded domains},
journal = {J. Comput. Appl. Math.},
year = {2008},
volume = {221},
number = {2},
pages = {376385},
doi = {10.1016/j.cam.2007.10.037}
}

M. Fornasier and F. Pitolli. Adaptive iterative thresholding algorithms for magnetoencephalography (MEG), J. Comput. Appl. Math., 221(2):386395, 2008.
[BibTeX] [.pdf]

BibTeX:
@article{MR2457671,
author = {Fornasier, Massimo and Pitolli, Francesca},
title = {Adaptive iterative thresholding algorithms for magnetoencephalography (MEG)},
journal = {J. Comput. Appl. Math.},
year = {2008},
volume = {221},
number = {2},
pages = {386395},
doi = {10.1016/j.cam.2007.10.048}
}

I. Daubechies, M. Fornasier and I. Loris. Accelerated projected gradient method for linear inverse problems with sparsity constraints, J. Fourier Anal. Appl., 14(56):764792, 2008.
[BibTeX] [.pdf]

BibTeX:
@article{MR2461606,
author = {Daubechies, Ingrid and Fornasier, Massimo and Loris, Ignace},
title = {Accelerated projected gradient method for linear inverse problems with sparsity constraints},
journal = {J. Fourier Anal. Appl.},
year = {2008},
volume = {14},
number = {56},
pages = {764792},
doi = {10.1007/s0004100890398}
}

2007  M. Fornasier. Banach frames for αmodulation spaces, Appl. Comput. Harmon. Anal., 22(2):157175, 2007.
[BibTeX] [.pdf]

BibTeX:
@article{MR2295293,
author = {Fornasier, Massimo},
title = {Banach frames for αmodulation spaces},
journal = {Appl. Comput. Harmon. Anal.},
year = {2007},
volume = {22},
number = {2},
pages = {157175},
doi = {10.1016/j.acha.2006.05.008}
}

S. Dahlke, M. Fornasier and T. Raasch. Adaptive frame methods for elliptic operator equations, Adv. Comput. Math., 27(1):2763, 2007.
[BibTeX] [.pdf]

BibTeX:
@article{MR2317920,
author = {Dahlke, Stephan and Fornasier, Massimo and Raasch, Thorsten},
title = {Adaptive frame methods for elliptic operator equations},
journal = {Adv. Comput. Math.},
year = {2007},
volume = {27},
number = {1},
pages = {2763},
doi = {10.1007/s1044400575016}
}

M. Fornasier and R. March. Restoration of color images by vector valued BV functions and variational calculus, SIAM J. Appl. Math., 68(2):437460, 2007.
[BibTeX] [.pdf]

BibTeX:
@article{MR2366993,
author = {Fornasier, Massimo and March, Riccardo},
title = {Restoration of color images by vector valued BV functions and variational calculus},
journal = {SIAM J. Appl. Math.},
year = {2007},
volume = {68},
number = {2},
pages = {437460},
doi = {10.1137/060671875}
}

S. Dahlke, T. Raasch, M. Werner, M. Fornasier and R. Stevenson. Adaptive frame methods for elliptic operator equations: the steepest descent approach, IMA J. Numer. Anal., 27(4):717740, 2007.
[BibTeX] [.pdf]

BibTeX:
@article{MR2371829,
author = {Dahlke, Stephan and Raasch, Thorsten and Werner, Manuel and Fornasier, Massimo and Stevenson, Rob},
title = {Adaptive frame methods for elliptic operator equations: the steepest descent approach},
journal = {IMA J. Numer. Anal.},
year = {2007},
volume = {27},
number = {4},
pages = {717740},
doi = {10.1093/imanum/drl035}
}

M. Fornasier. Domain decomposition methods for linear inverse problems with sparsity constraints, Inverse Problems, 23(6):25052526, 2007.
[BibTeX] [.pdf]

BibTeX:
@article{MR2441016,
author = {Fornasier, Massimo},
title = {Domain decomposition methods for linear inverse problems with sparsity constraints},
journal = {Inverse Problems},
year = {2007},
volume = {23},
number = {6},
pages = {25052526},
doi = {10.1088/02665611/23/6/014}
}

2006  H.G. Feichtinger and M. Fornasier. Flexible Gaborwavelet atomic decompositions for L^2Sobolev spaces, Ann. Mat. Pura Appl. (4), 185(1):105131, 2006.
[BibTeX] [.pdf]

BibTeX:
@article{MR2179584,
author = {Feichtinger, Hans G. and Fornasier, Massimo},
title = {Flexible Gaborwavelet atomic decompositions for L^2Sobolev spaces},
journal = {Ann. Mat. Pura Appl. (4)},
year = {2006},
volume = {185},
number = {1},
pages = {105131},
doi = {10.1007/s1023100401308}
}

M. Fornasier. Nonlinear projection recovery in digital inpainting for color image restoration, J. Math. Imaging Vision, 24(3):359373, 2006.
[BibTeX]

BibTeX:
@article{MR2235479,
author = {Fornasier, Massimo},
title = {Nonlinear projection recovery in digital inpainting for color image restoration},
journal = {J. Math. Imaging Vision},
year = {2006},
volume = {24},
number = {3},
pages = {359373},
doi = {10.1007/s1085100642421}
}

M. Fornasier. On some stability results of localized atomic decompositions, Rend. Mat. Appl. (7), 26(34):315325, 2006.
[BibTeX]

BibTeX:
@article{MR2294197,
author = {Fornasier, Massimo},
title = {On some stability results of localized atomic decompositions},
journal = {Rend. Mat. Appl. (7)},
year = {2006},
volume = {26},
number = {34},
pages = {315325},
doi = {http://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2006(34)/315325.pdf}
}

2005  M. Fornasier and D. Toniolo. Fast, robust and efficient 2D pattern recognition for reassembling fragmented images, Pattern Recognition, 38(11):20742087, 2005.
[Abstract] [BibTeX] [.pdf]

Abstract We discuss the realization of a fast, robust and accurate pattern matching algorithm for comparison of digital images implemented by discrete Circular Harmonic expansions based on sampling theory. The algorithm and its performance for reassembling fragmented digital images are described in detail and illustrated by examples and data from the experimentation on an art fresco real problem. Because of the huge database of patterns and the largescale dimension, the results of the experimentation are relevant to describe the power of discrimination and the efficiency of such method. 
BibTeX:
@article{Fornasier20052074,
author = {Massimo Fornasier and Domenico Toniolo},
title = {Fast, robust and efficient 2D pattern recognition for reassembling fragmented images},
journal = {Pattern Recognition},
year = {2005},
volume = {38},
number = {11},
pages = {20742087},
doi = {10.1016/j.patcog.2005.03.014}
}

M. Fornasier and K. Gröchenig. Intrinsic localization of frames, Constr. Approx., 22(3):395415, 2005.
[BibTeX] [.pdf]

BibTeX:
@article{MR2164142,
author = {Fornasier, Massimo and Gröchenig, Karlheinz},
title = {Intrinsic localization of frames},
journal = {Constr. Approx.},
year = {2005},
volume = {22},
number = {3},
pages = {395415},
doi = {10.1007/s0036500405923}
}

M. Fornasier and H. Rauhut. Continuous frames, function spaces, and the discretization problem, J. Fourier Anal. Appl., 11(3):245287, 2005.
[BibTeX] [.pdf]

BibTeX:
@article{MR2167169,
author = {Fornasier, Massimo and Rauhut, Holger},
title = {Continuous frames, function spaces, and the discretization problem},
journal = {J. Fourier Anal. Appl.},
year = {2005},
volume = {11},
number = {3},
pages = {245287},
doi = {10.1007/s0004100540536}
}

M. Morandi Cecchi and M. Fornasier. Fast homogenization algorithm based on asymptotic theory and multiscale schemes, Numer. Algorithms, 40(2):171186, 2005.
[BibTeX]

BibTeX:
@article{MR2189166,
author = {Morandi Cecchi, Maria and Fornasier, Massimo},
title = {Fast homogenization algorithm based on asymptotic theory and multiscale schemes},
journal = {Numer. Algorithms},
year = {2005},
volume = {40},
number = {2},
pages = {171186},
doi = {10.1007/s1107500515306}
}

2004  M. Fornasier. Quasiorthogonal decompositions of structured frames, J. Math. Anal. Appl., 289(1):180199, 2004.
[BibTeX]

BibTeX:
@article{MR2020535,
author = {Fornasier, Massimo},
title = {Quasiorthogonal decompositions of structured frames},
journal = {J. Math. Anal. Appl.},
year = {2004},
volume = {289},
number = {1},
pages = {180199},
doi = {10.1016/j.jmaa.2003.09.041}
}

2003  M. Fornasier. Function spaces inclusions and rate of convergence of Riemanntype sums in numerical integration, Numer. Funct. Anal. Optim., 24(12):4557, 2003.
[BibTeX] [.pdf]

BibTeX:
@article{MR1978950,
author = {Fornasier, Massimo},
title = {Function spaces inclusions and rate of convergence of Riemanntype sums in numerical integration},
journal = {Numer. Funct. Anal. Optim.},
year = {2003},
volume = {24},
number = {12},
pages = {4557},
doi = {10.1081/NFA120020243}
}


back to top 
Conference Papers 
C. Kümmerle and C. Mayrink Verdun. Denoising and Completion of Structured LowRank Matrices via Iteratively Reweighted Least Squares ^{}, In International Traveling Workshop on Interactions between LowComplexity Data Models and Sensing Techniques (iTWIST), Marseille, France, 2018.
[Abstract] [BibTeX]

Abstract We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of completing or denoising lowrank matrices that are structured, e.g., that possess a Hankel, Toeplitz or blockHankel/Toeplitz structure. The algorithm optimizes an objective based on a nonconvex surrogate of the rank by solving a sequence of quadratic problems. Our strategy combines computational efficiency, as it operates on a lower dimensional generator space of the structured matrices, with high statistical accuracy which can be observed in experiments on hard estimation and completion tasks. Our experiments show that the proposed algorithm StrucHMIRLS exhibits an empirical recovery probability close to 1 from fewer samples than the stateoftheart in a Hankel matrix completion task arising from the problem of spectral superresolution of badly separated frequencies. Furthermore, we explain how the proposed algorithm for structured lowrank recovery can be used as preprocessing step for improved robustness in frequency or line spectrum estimation problems. 
BibTeX:
@inproceedings{KV18_iTwist18,
author = {C. Kümmerle and C. Mayrink Verdun},
title = {Denoising and Completion of Structured LowRank Matrices via Iteratively Reweighted Least Squares},
booktitle = {International Traveling Workshop on Interactions between LowComplexity Data Models and Sensing Techniques (iTWIST), Marseille, France},
year = {2018}
}

M. Morandotti. Structured Deformations of Continua: Theory and Applications, In Proceedings of the Conference CoMFoS16, to appear.
[Abstract] [BibTeX] [arXiv]

Abstract The scope of this contribution is to present an overview of the theory of structured deformations of continua, together with some applications. Structured deformations aim at being a unified theory in which elastic and plastic behaviours, as well as fractures and defects can be described in a single setting. Since its introduction in the scientific community of rational mechanicists (Del PieroOwen, ARMA 1993), the theory has been put in the framework of variational calculus (ChoksiFonseca, ARMA 1997), thus allowing for solution of problems via energy minimization. Some background, three problems and a discussion on future directions are presented. 
BibTeX:
@inproceedings{Morandotti17,
author = {Morandotti, M.},
title = {Structured Deformations of Continua: Theory and Applications},
booktitle = {Proceedings of the Conference CoMFoS16},
year = {to appear},
url = {https://arxiv.org/abs/1702.02105}
}

M. Morandotti. Qualitative and quantitative properties of the dynamics of screw dislocations, In Proceedings on the XXIII Congresso AIMETA, to appear.
[Abstract] [BibTeX] [arXiv]

Abstract This note collects some results on the behaviour of screw dislocation in an elastic medium. By using a semidiscrete model, we are able to investigate two specific aspects of the dynamics, namely (i) the interaction with free boundaries and collision events and (ii) the confinement inside the domain when a suitable Dirichlettype boundary condition is imposed. In the first case, we analytically prove that free boundaries attract dislocations and we provide an expression for the PeachKoehler force on a dislocation near the boundary. Moreover, we use this to prove an upper bound on the collision time of a dislocation with the boundary, provided certain geometric conditions are satisfied. An upper bound on the collision time for two dislocations with opposite Burgers vectors hitting each other is also obtained. In the second case, we turn to domains whose boundaries are subject to an external stress. In this situation, we prove that dislocations find it energetically favourable to stay confined inside the material instead of getting closer to the boundary. The result first proved for a single dislocation in the material is extended to a system of many dislocations, for which the analysis requires the careful treatments of the interaction terms. 
BibTeX:
@inproceedings{Morandotti173,
author = {Morandotti, M.},
title = {Qualitative and quantitative properties of the dynamics of screw dislocations},
booktitle = {Proceedings on the XXIII Congresso AIMETA},
year = {to appear},
url = {https://arxiv.org/abs/1707.06176}
}

C. Kümmerle and J. Sigl. Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery, In 12th International Conference on Sampling Theory and Applications (SampTA), pp. 489493, 2017.
[BibTeX]

BibTeX:
@inproceedings{HMIRLS_SampTA17,
author = {C. Kümmerle and J. Sigl},
title = {Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery},
booktitle = {12th International Conference on Sampling Theory and Applications (SampTA)},
year = {2017},
pages = {489493}
}

P. Burgholzer, M. Sandbichler, F. Krahmer, T. Berer and M. Haltmeier. Sparsifying transformations of photoacoustic signals enabling compressed sensing algorithms, Proc. SPIE, In , 9708, pp. 9708289708288, 2016.
[Abstract] [BibTeX] [doi]

Abstract Compressed sensing allows performing much fewer measurements than advised by the Shannon sampling theory. This is surprising because it requires the solution of a system of equations with much fewer equations than unknowns. This is possible if one can assume sparsity of the solution, which means that only a few components of the solution are significantly different from zero. An important ingredient for compressed sensing is the restricted isometry property (RIP) of the sensing matrix, which is satisfied for certain types of random measurement ensembles. Then a sparse solution can be found by minimizing the ℓ1norm. Using standard approaches, photoacoustic imaging generally neither satisfies sparsity of the data nor the RIP. Therefore, no theoretical recovery guarantees could be given. Despite ℓ1 minimization has been used for photoacoustic image reconstruction, only marginal improvements in comparison to classical photoacoustic reconstruction have been observed. We propose the application of a sparsifying temporal transformation to the detected pressure signals, which allows obtaining theoretical recovery guarantees for our compressed sensing scheme. Such a sparsifying transform can be found because spatial and temporal evolution of the pressure wave are not independent, but connected by the wave equation. We give an example of a sparsifying transform and apply our compressed sensing scheme to reconstruct images from simulated data.

BibTeX:
@inproceedings{doi:10.1117/12.2209301,
author = {Burgholzer, P. and Sandbichler, M. and Krahmer, F. and Berer, T. and Haltmeier, M.},
title = {Sparsifying transformations of photoacoustic signals enabling compressed sensing algorithms},
journal = {Proc. SPIE},
year = {2016},
volume = {9708},
pages = {9708289708288},
doi = {10.1117/12.2209301}
}

G. Albi, L. Pareschi and M. Zanella. On the Optimal Control of Opinion Dynamics on Evolving Networks, In L. Bociu, J.A. Désidéri and A. Habbal, (Ed.) Conference on System Modeling and Optimization (CSMO 2015), Springer International Publishing Cham, pp. 5867, 2015.
[Abstract] [BibTeX] [arXiv] [doi]

Abstract In this work we are interested in the modelling and control of opinion dynamics spreading on a time evolving network with scalefree asymptotic degree distribution. The mathematical model is formulated as a coupling of an opinion alignment system with a probabilistic description of the network. The optimal control problem aims at forcing consensus over the network, to this goal a control strategy based on the degree of connection of each agent has been designed. A numerical method based on a model predictive strategy is then developed and different numerical tests are reported. The results show that in this way it is possible to drive the overall opinion toward a desired state even if we control only a suitable fraction of the nodes. 
BibTeX:
@inproceedings{2015arXiv151100145A,
author = {Albi, Giacomo and Pareschi, Lorenzo and Zanella, Mattia},
editor = {Bociu, Lorena and Désidéri, JeanAntoine and Habbal, Abderrahmane},
title = {On the Optimal Control of Opinion Dynamics on Evolving Networks},
booktitle = {Conference on System Modeling and Optimization (CSMO 2015)},
publisher = {Springer International Publishing},
year = {2015},
pages = {5867},
url = {http://arxiv.org/abs/1511.00145},
doi = {10.1007/9783319557953_4}
}

M. Bongini, M. Fornasier, F. Fröhlich and L. Haghverdi. Sparse control of force field dynamics, In Proceedings of the International Conference on Network Games, Control and Optimization., 2014.
[BibTeX]

BibTeX:
@inproceedings{BFFH14,
author = {M. Bongini and M. Fornasier and F. Fröhlich and L. Haghverdi},
title = {Sparse control of force field dynamics},
booktitle = {Proceedings of the International Conference on Network Games, Control and Optimization.},
year = {2014}
}

W. Baatz, M. Fornasier and J. Haskovec. Mathematical Methods for Spectral Image Reconstruction, In G.H. Bock, W. Jäger and J.M. Winckler, (Ed.) Proceedings of the workshop Scientific Computing and Cultural Heritage: Contributions in Computational Humanities, November 2009, Springer Berlin Heidelberg, pp. 310, 2013.
[BibTeX] [doi]

BibTeX:
@inproceedings{BFH13,
author = {Baatz, Wolfgang and Fornasier, Massimo and Haskovec, Jan},
editor = {Bock, Georg Hans and Jäger, Willi and Winckler, J. Michael},
title = {Mathematical Methods for Spectral Image Reconstruction},
booktitle = {Proceedings of the workshop Scientific Computing and Cultural Heritage: Contributions in Computational Humanities, November 2009},
publisher = {Springer Berlin Heidelberg},
year = {2013},
pages = {310},
doi = {10.1007/9783642280214_1}
}

G. Bretti, M. Fornasier and F. Pitolli. Electric current density imaging via an accelerated iterative algorithm with joint sparsity constraints, In Ré. Gribonval, (Ed.) SPARS'09  Signal Processing with Adaptive Sparse Structured Representations Saint Malo, France, 2009.
[BibTeX]

BibTeX:
@inproceedings{bretti:inria00369432,
author = {Bretti, Gabriella and Fornasier, Massimo and Pitolli, Francesca},
editor = {Rémi Gribonval},
title = {Electric current density imaging via an accelerated iterative algorithm with joint sparsity constraints},
booktitle = {SPARS'09  Signal Processing with Adaptive Sparse Structured Representations},
year = {2009}
}

W. Baatz, M. Fornasier, P.A. Markowich and C.B. Schönlieb. Binary Based Fresco Restoration, In C.S. Kaplan and R. Sarhangi, (Ed.) Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture, Tarquin Publications London, pp. 337338, 2009.
[BibTeX]

BibTeX:
@inproceedings{bridges2009:337,
author = {Wolfgang Baatz and Massimo Fornasier and Peter A. Markowich and CarolaBibiane Schönlieb},
editor = {Craig S. Kaplan and Reza Sarhangi},
title = {Binary Based Fresco Restoration},
booktitle = {Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture},
publisher = {Tarquin Publications},
year = {2009},
pages = {337338},
note = {Available online at http://archive.bridgesmathart.org/2009/bridges2009337.html}
}

M. Fornasier. Compressive AlgorithmsAdaptive Solutions of PDEs and Variational Problems, In E.R. Hancock, R.R. Martin and M.A. Sabin, (Ed.) Mathematics of Surfaces XIII: 13th IMA International Conference York, UK, September 79, 2009 Proceedings, Springer Berlin Heidelberg Berlin, Heidelberg, pp. 143169, 2009.
[BibTeX] [doi]

BibTeX:
@incollection{F09,
author = {Fornasier, M.},
editor = {Hancock, Edwin R. and Martin, Ralph R. and Sabin, Malcolm A.},
title = {Compressive AlgorithmsAdaptive Solutions of PDEs and Variational Problems},
booktitle = {Mathematics of Surfaces XIII: 13th IMA International Conference York, UK, September 79, 2009 Proceedings},
publisher = {Springer Berlin Heidelberg},
year = {2009},
pages = {143169},
doi = {10.1007/9783642035968_9}
}

M. Fornasier, A. Langer and C.B. Schönlieb. Domain decomposition methods for compressed sensing, In Proceedings of the 8th International Conference on Sampling Theory and Applications, 2009.
[BibTeX] [arXiv]

BibTeX:
@inproceedings{FLS09,
author = {Massimo Fornasier and Andreas Langer and CarolaBibiane Schönlieb},
title = {Domain decomposition methods for compressed sensing},
booktitle = {Proceedings of the 8th International Conference on Sampling Theory and Applications},
year = {2009},
url = {http://arxiv.org/abs/0902.0124}
}

I. Daubechies, R. DeVore, M. Fornasier and C.S. Güntürk. Iteratively Reweighted Least Squares minimization: Proof of faster than linear rate for sparse recovery, In Information Sciences and Systems, 2008. CISS 2008. 42nd Annual Conference on, pp. 2629, 2008.
[Abstract] [BibTeX] [doi]

Abstract Given an mtimesN matrix Phi, with m<N, the system of equations Phix=y is typically underdetermined and has infinitely many solutions. Various forms of optimization can extract a "best" solution. One of the oldest is to select the one with minimal lscr2 norm. It has been shown that in many applications a better choice is the minimal lscr1 norm solution. This is the case in compressive sensing, when sparse solutions are sought. The minimal lscr1 norm solution can be found by using linear programming; an alternative method is iterative reweighted least squares (IRLS), which in some cases is numerically faster. The main step of IRLS finds, for a given weight w, the solution with smallest lscr2(w) norm; this weight is updated at every iteration step: if x(n) is the solution at step n, then w(n) is defined by wi (n):=1/xi (n), i=1,...,N. We give a specific recipe for updating weights that avoids technical shortcomings in other approaches, and for which we can prove convergence under certain conditions on the matrix Phi known as the restricted isometry property. We also show that if there is a sparse solution, then the limit of the proposed algorithm is that sparse solution. It is also shown that whenever the solution at a given iteration is sufficiently close to the limit, then the remaining steps of the algorithm converge exponentially fast. In the standard version of the algorithm, designed to emulate lscr1minimization, the exponential rate is linear; in adapted versions aimed at lscrtauminimization with tau<1, we prove faster than linear rate. 
BibTeX:
@inproceedings{4558489,
author = {I. Daubechies and R. !DeVore and M. Fornasier and Güntürk, C. Sinan},
title = {Iteratively Reweighted Least Squares minimization: Proof of faster than linear rate for sparse recovery},
booktitle = {Information Sciences and Systems, 2008. CISS 2008. 42nd Annual Conference on},
year = {2008},
pages = {2629},
doi = {10.1109/CISS.2008.4558489}
}

P.A.M. Wolfgang Baatz Massimo Fornasier and C.B. Schönlieb. Inpainting of Ancient Austrian Frescoes, In R. Sarhangi and C.H. Séquin, (Ed.) Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture, Tarquin Publications London, pp. 163170, 2008.
[BibTeX]

BibTeX:
@inproceedings{bridges2008:163,
author = {Wolfgang Baatz, Massimo Fornasier, Peter A. Markowich and and CarolaBibiane Schönlieb},
editor = {Reza Sarhangi and Carlo H. Séquin},
title = {Inpainting of Ancient Austrian Frescoes},
booktitle = {Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture},
publisher = {Tarquin Publications},
year = {2008},
pages = {163170},
note = {Available online at http://archive.bridgesmathart.org/2008/bridges2008163.html}
}

M. Fornasier. Faithful Recovery of Vector Valued Functions from Incomplete Data: Recolorization and Art Restoration, In Proceedings of the 1st International Conference on Scale Space and Variational Methods in Computer Vision, SpringerVerlag Berlin, Heidelberg, pp. 116127, 2007.
[BibTeX] [doi]

BibTeX:
@inproceedings{Fornasier:2007:FRV:1767926.1767939,
author = {Fornasier, Massimo},
title = {Faithful Recovery of Vector Valued Functions from Incomplete Data: Recolorization and Art Restoration},
booktitle = {Proceedings of the 1st International Conference on Scale Space and Variational Methods in Computer Vision},
publisher = {SpringerVerlag},
year = {2007},
pages = {116127},
doi = {10.1007/9783540728238_11}
}

M. Fornasier and L. Gori. On elementary sampling theorems on bounded domains, In ICNAAM 2005. International conference on numerical analysis and applied mathematics 2005. Official conference of the European Society of Computational Methods in Sciences and Engineering (ESCMSE), Rhodes, Greek, September 1620, 2005., Weinheim: WileyVCH, pp. 619623, 2005.
[BibTeX]

BibTeX:
@incollection{zbMATH05008377,
author = {Massimo Fornasier and Laura Gori},
title = {On elementary sampling theorems on bounded domains},
booktitle = {ICNAAM 2005. International conference on numerical analysis and applied mathematics 2005. Official conference of the European Society of Computational Methods in Sciences and Engineering (ESCMSE), Rhodes, Greek, September 1620, 2005.},
publisher = {Weinheim: WileyVCH},
year = {2005},
pages = {619623}
}

M. Fornasier. Building a bridge between Gabor and wavelet worlds, Oberwolfach Reports, In H. Feichtinger, P. Jorgensen, D. Larson and G. Olafsson, (Ed.) Oberwolfach Reports, MiniWorkshop: Wavelets and Frames, 1(1), pp. 479544, 2004.
[BibTeX]

BibTeX:
@inproceedings{feichtinger2004mini,
author = {Massimo Fornasier},
editor = {Feichtinger, H and Jorgensen, P and Larson, Dave and Olafsson, Gestur},
title = {Building a bridge between Gabor and wavelet worlds},
booktitle = {Oberwolfach Reports, MiniWorkshop: Wavelets and Frames},
journal = {Oberwolfach Reports},
year = {2004},
volume = {1},
number = {1},
pages = {479544}
}

M. Fornasier. Decompositions of Hilbert spaces: local construction of global frames, In Constructive theory of functions, DARBA, Sofia, pp. 275281, 2003.
[BibTeX]

BibTeX:
@incollection{MR2092351,
author = {Fornasier, Massimo},
title = {Decompositions of Hilbert spaces: local construction of global frames},
booktitle = {Constructive theory of functions},
publisher = {DARBA, Sofia},
year = {2003},
pages = {275281}
}


back to top 
Book Chapters 
M. Bongini and M. Fornasier. Sparse Control of Multiagent Systems, In: Active Particles, Volume 1 : Advances in Theory, Models, and Applications, N. Bellomo, P. Degond and E. Tadmor (ed.), Springer International Publishing Cham, pp. 173228, 2017.
[Abstract] [BibTeX] [doi]

Abstract In recent years, numerous studies have focused on the mathematical modeling of social dynamics, with selforganization, i.e., the autonomous pattern formation, as the main driving concept. Usually, first or secondorder models are employed to reproduce, at least qualitatively, certain global patterns (such as bird flocking, milling schools of fish, or queue formations in pedestrian flows, just to mention a few). It is, however, common experience that selforganization does not always spontaneously occur in a society. In this review chapter, we aim to describe the limitations of decentralized controls in restoring certain desired configurations and to address the question of whether it is possible to externally and parsimoniously influence the dynamics to reach a given outcome. More specifically, we address the issue of finding the sparsest control strategy for finite agentbased models in order to lead the dynamics optimally toward a desired pattern. 
BibTeX:
@inbook{BF17,
author = {Bongini, Mattia and Fornasier, Massimo},
editor = {Bellomo, Nicola and Degond, Pierre and Tadmor, Eitan},
title = {Sparse Control of Multiagent Systems},
booktitle = {Active Particles, Volume 1 : Advances in Theory, Models, and Applications},
publisher = {Springer International Publishing},
year = {2017},
pages = {173228},
doi = {10.1007/9783319499963_5}
}

J. A. Carrillo, Y.P. Choi, and S. Pérez. Active Particles Vol. I  Theory, Models, Applications, preprint, N. Bellomo P. Degond and E. Tadmor (ed.), BirkhäuserSpringer, to appear.
[BibTeX] [.pdf]

BibTeX:
@inbook{CCP16,
author = {J. A. Carrillo, Y.P. Choi, and S. Pérez},
editor = {N. Bellomo, P. Degond, and E. Tadmor},
title = {Active Particles Vol. I  Theory, Models, Applications},
journal = {preprint},
publisher = {BirkhäuserSpringer},
year = {to appear},
url = {https://arxiv.org/abs/1605.00232}
}

Y.P. Choi, S.Y. Ha and Z. Li. Active Particles Vol. I  Theory, Models, Applications, preprint, N. Bellomo P. Degond and E. Tadmor (ed.), BirkhäuserSpringer, to appear.
[BibTeX] [.pdf]

BibTeX:
@inbook{CHL16,
author = {Y.P. Choi and S.Y. Ha, and Z. Li},
editor = {N. Bellomo, P. Degond, and E. Tadmor},
title = {Active Particles Vol. I  Theory, Models, Applications},
journal = {preprint},
publisher = {BirkhäuserSpringer},
year = {to appear},
url = {http://arxiv.org/abs/1604.04887}
}

M. Fornasier and H. Rauhut. Handbook of Mathematical Methods in Imaging, O. Scherzer (ed.), Springer New York New York, NY, pp. 205256, 2015.
[BibTeX] [doi]

BibTeX:
@inbook{Fornasier2015,
author = {Fornasier, Massimo and Rauhut, Holger},
editor = {Scherzer, Otmar},
title = {Handbook of Mathematical Methods in Imaging},
publisher = {Springer New York},
year = {2015},
pages = {205256},
doi = {10.1007/9781493907908_6}
}

M. Fornasier and S. Peter. An Overview on Algorithms for Sparse Recovery, In: Sparse Reconstruction and Compressive Sensing in Remote Sensing, X. Zhu and R. Bamler (ed.), Springer, 2015.
[BibTeX]

BibTeX:
@incollection{FP15,
author = {Massimo Fornasier and Steffen Peter},
editor = {X. Zhu and R. Bamler},
title = {An Overview on Algorithms for Sparse Recovery},
booktitle = {Sparse Reconstruction and Compressive Sensing in Remote Sensing},
publisher = {Springer},
year = {2015}
}

M. Artina, M. Fornasier, S. Micheletti and S. Perotto. The benefits of anisotropic mesh adaptation for brittle fractures under planestrain conditions, In: New challenges in grid generation and adaptivity for scientific computing, 5, Springer, Cham, pp. 4367, 2015.
[BibTeX] [doi]

BibTeX:
@incollection{MR3362235,
author = {Artina, Marco and Fornasier, Massimo and Micheletti, Stefano and Perotto, Simona},
title = {The benefits of anisotropic mesh adaptation for brittle fractures under planestrain conditions},
booktitle = {New challenges in grid generation and adaptivity for scientific computing},
publisher = {Springer, Cham},
year = {2015},
volume = {5},
pages = {4367},
doi = {10.1007/9783319060538_3}
}

M. Artina, M. Fornasier, S. Micheletti and S. Perotto. Anisotropic adaptive meshes for brittle fractures: parameter sensitivity., In: Numerical mathematics and advanced applications  ENUMATH 2013. Proceedings of ENUMATH 2013, the 10th European conference on numerical mathematics and advanced applications, Lausanne, Switzerland, August 2630, 2013, Cham: Springer, pp. 293301, 2015.
[BibTeX] [doi]

BibTeX:
@incollection{zbMATH06466204,
author = {Marco Artina and Massimo Fornasier and Stefano Micheletti and Simona Perotto},
title = {Anisotropic adaptive meshes for brittle fractures: parameter sensitivity.},
booktitle = {Numerical mathematics and advanced applications  ENUMATH 2013. Proceedings of ENUMATH 2013, the 10th European conference on numerical mathematics and advanced applications, Lausanne, Switzerland, August 2630, 2013},
publisher = {Cham: Springer},
year = {2015},
pages = {293301},
doi = {10.1007/9783319107059_29}
}

M. Fornasier. Numerical methods for sparse recovery, In: Theoretical foundations and numerical methods for sparse recovery, M. Fornasier (ed.), 9, Walter de Gruyter, Berlin, pp. 93200, 2010.
[BibTeX] [doi]

BibTeX:
@incollection{MR2731598,
author = {Fornasier, Massimo},
editor = {Fornasier, Massimo},
title = {Numerical methods for sparse recovery},
booktitle = {Theoretical foundations and numerical methods for sparse recovery},
publisher = {Walter de Gruyter, Berlin},
year = {2010},
volume = {9},
pages = {93200},
doi = {10.1515/9783110226157.93}
}

J.A. Carrillo, M. Fornasier, G. Toscani and F. Vecil. Particle, kinetic, and hydrodynamic models of swarming, In: Mathematical modeling of collective behavior in socioeconomic and life sciences, Birkhäuser Boston, Inc., Boston, MA, pp. 297336, 2010.
[BibTeX] [doi]

BibTeX:
@incollection{MR2744704,
author = {Carrillo, José A. and Fornasier, Massimo and Toscani, Giuseppe and Vecil, Francesco},
title = {Particle, kinetic, and hydrodynamic models of swarming},
booktitle = {Mathematical modeling of collective behavior in socioeconomic and life sciences},
publisher = {Birkhäuser Boston, Inc., Boston, MA},
year = {2010},
pages = {297336},
doi = {10.1007/9780817649463_12}
}

M. Fornasier. Mathknow: Mathematics, Applied Sciences and Real Life, M. Emmer and A. Quarteroni (ed.), Springer Milan Milano, pp. 217228, 2009.
[BibTeX] [doi]

BibTeX:
@inbook{mathsinpict09,
author = {Fornasier, Massimo},
editor = {Emmer, Michele and Quarteroni, Alfio},
title = {Mathknow: Mathematics, Applied Sciences and Real Life},
publisher = {Springer Milan},
year = {2009},
pages = {217228},
doi = {10.1007/9788847011229_17}
}

M. Fornasier, R. Cazzato, G. Costa, A.D. Farra, D. Toniolo, D. Tosato and C. Zanuso. Andrea Mantegna. La Cappella Ovetari a Padova, D.T. Anna Maria Spiazzi Alberta De Nicolo' Salmazo (ed.), Skira, 2006.
[BibTeX]

BibTeX:
@inbook{progetto2006,
author = {M. Fornasier and R. Cazzato and G. Costa and A. Dal Farra and D. Toniolo and D. Tosato and C. Zanuso},
editor = {Anna Maria Spiazzi, Alberta De Nicolo' Salmazo, Domenico Toniolo},
title = {Andrea Mantegna. La Cappella Ovetari a Padova},
publisher = {Skira},
year = {2006}
}

M. Fornasier and D. Toniolo. Mantegna nella chiesa degli Eremitani a Padova. Il recupero possibile, A.M.S. et al. null (ed.), Skira, pp. 1523, 2003.
[BibTeX]

BibTeX:
@inbook{mantegna03,
author = {M. Fornasier and D. Toniolo},
editor = {Anna Maria Spiazzi et al.},
title = {Mantegna nella chiesa degli Eremitani a Padova. Il recupero possibile},
publisher = {Skira},
year = {2003},
pages = {1523}
}


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PhD Theses 
S. Peter. Algorithms for Robust and Fast Sparse Recovery. Technische Universität München, 2016.
[BibTeX]

BibTeX:
@phdthesis{PeterThesis16,
author = {Peter, Steffen},
title = {Algorithms for Robust and Fast Sparse Recovery},
school = {Technische Universität München},
year = {2016},
url = {https://mediatum.ub.tum.de/doc/1295426/1295426.pdf}
}

M. Bongini. Sparse Optimal Control of Multiagent Systems. Technische Universität München, 2016.
[BibTeX]

BibTeX:
@phdthesis{BonginiThesis16,
author = {Bongini, Mattia},
title = {Sparse Optimal Control of Multiagent Systems},
school = {Technische Universität München},
year = {2016},
url = {https://mediatum.ub.tum.de/doc/1303123/1303123.pdf}
}

M. Artina. Lagrangian Methods for Constrained NonConvex Minimizations and Applications in Fracture Mechanics. Technische Universität München, 2015.
[BibTeX]

BibTeX:
@phdthesis{ArtinaThesis15,
author = {Artina, Marco},
title = {Lagrangian Methods for Constrained NonConvex Minimizations and Applications in Fracture Mechanics},
school = {Technische Universität München},
year = {2015},
url = {https://mediatum.ub.tum.de/doc/1275879/1275879.pdf}
}

F. Krahmer. Novel Schemes for SigmaDelta Modulation: From Improved Exponential Accuracy to LowComplexity Design. New York University, 2009.
[BibTeX] [.pdf]

BibTeX:
@phdthesis{KrThesis,
author = {Felix Krahmer},
title = {Novel Schemes for SigmaDelta Modulation: From Improved Exponential Accuracy to LowComplexity Design},
school = {New York University},
year = {2009},
url = {http://num.math.unigoettingen.de/~f.krahmer/Thesis_Felix_Krahmer.pdf}
}

M. Fornasier. Compressive Algorithms. Adaptive Solutions of PDE's and Variational Problems, Habilitationsschrift. Faculty of Mathematics, University of Vienna, 2008.
[BibTeX]

BibTeX:
@phdthesis{Fhabil08,
author = {Massimo Fornasier},
title = {Compressive Algorithms. Adaptive Solutions of PDE's and Variational Problems},
school = {Faculty of Mathematics, University of Vienna},
year = {2008},
note = {Habilitationsschrift}
}

M. Fornasier. Constructive methods for numerical applications in signal processing and homogenization problems. University of Padova and University of Vienna, 2002.
[BibTeX]

BibTeX:
@phdthesis{fornasier2002constructive,
author = {Fornasier, Massimo},
title = {Constructive methods for numerical applications in signal processing and homogenization problems},
school = {University of Padova and University of Vienna},
year = {2002}
}


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Miscellaneous 
F. Krahmer, C. Kümmerle and H. Rauhut. A Quotient Property for Matrices with HeavyTailed Entries and its Application to NoiseBlind Compressed Sensing, 2018.
[Abstract] [BibTeX] [arXiv]

Abstract For a large class of random matrices A with i.i.d. entries we show that the 1quotient property holds with probability exponentially close to 1. In contrast to previous results, our analysis does not require concentration of the entrywise distributions. We provide a unified proof that recovers corresponding previous re sults for (sub)Gaussian and Weibull distributions. Our findings generalize known results on the geometry of random polytopes, providing lower bounds on the size of the largest Euclidean ball contained in the centrally symmetric polytope spanned by the columns of A. At the same time, our results establish robustness of noiseblind l1decoders for recovering sparse vectors x from underdetermined, noisy linear measurements y=Ax+w under the weakest possible assumptions on the entrywise distributions that allow for recovery with optimal sample complexity even in the noiseless case. Our analysis predicts superior robustness behavior for measurement matrices with superGaussian entries, which we confirm by numerical experiments. 
BibTeX:
@unpublished{KrahmerKuemmerleRauhut18,
author = {Felix Krahmer, Christian Kümmerle, Holger Rauhut},
title = {A Quotient Property for Matrices with HeavyTailed Entries and its Application to NoiseBlind Compressed Sensing},
year = {2018},
doi = {https://arxiv.org/abs/1806.04261}
}

M. Burr, F. Krahmer and C. Yap. Continuous Amortization: A nonprobabilistic adaptive analysis technique, Technical report. Electronic Colloquium on Computational Complexity, 2009.
[BibTeX]

BibTeX:
@techreport{BuKrYa09,
author = {Burr, Michael and Krahmer, Felix and Yap, Chee},
title = {Continuous Amortization: A nonprobabilistic adaptive analysis technique},
school = {Electronic Colloquium on Computational Complexity},
year = {2009},
note = {Technical report}
}

F. Krahmer, G. Pfander and P. Rashkov. Support size conditions for timefrequency representations on finite Abelian groups, Technical report. Jacobs University, Bremen, 2007.
[BibTeX]

BibTeX:
@techreport{KraPfaRa07,
author = {Krahmer, F. and Pfander, G. and Rashkov, P.},
title = {Support size conditions for timefrequency representations on finite Abelian groups},
school = {Jacobs University, Bremen},
year = {2007},
note = {Technical report}
}

M. Fornasier. Introduzione all'analisi armonica numerica (Italian), Lecture notes, 2003.
[BibTeX]

BibTeX:
@misc{analisiarmonicanumerica03,
author = {Massimo Fornasier},
title = {Introduzione all'analisi armonica numerica (Italian)},
year = {2003},
note = {Lecture notes}
}

M.F. C. Fanin and D. Toniolo. Proposta per una anastilosi informatica degli affreschi della Cappella Ovetari nella Chiesa degli Eremitani in Padova (Italian), Technical report DFPD 02/EI/31. Department of Physics "G. Galilei", University of Padua, 2002.
[BibTeX]

BibTeX:
@techreport{FFT02,
author = {C. Fanin, M. Fornasier and D. Toniolo},
title = {Proposta per una anastilosi informatica degli affreschi della Cappella Ovetari nella Chiesa degli Eremitani in Padova (Italian)},
school = {Department of Physics "G. Galilei", University of Padua},
year = {2002},
number = {DFPD 02/EI/31},
note = {Technical report}
}

M. Fornasier and D. Toniolo. Compactly supported circular harmonics: fast, robust and efficient 2D pattern recognition, Technical report DFPD 02/EI/32. Department of Physics "G. Galilei", University of Padua, 2002.
[BibTeX]

BibTeX:
@techreport{FT2002,
author = {M. Fornasier and D. Toniolo},
title = {Compactly supported circular harmonics: fast, robust and efficient 2D pattern recognition},
school = {Department of Physics "G. Galilei", University of Padua},
year = {2002},
number = {DFPD 02/EI/32},
note = {Technical report}
}

M. Fornasier. Un metodo per la rappresentazione e il confronto di immagini a meno di rotazioni. Un contributo alla ricostruzione virtuale degli affreschi della Chiesa degli Eremitani in Padova (Italian). Department of Pure and Applied Mathematics, University of Padua, 1999.
[BibTeX]

BibTeX:
@mastersthesis{F99,
author = {Massimo Fornasier},
title = {Un metodo per la rappresentazione e il confronto di immagini a meno di rotazioni. Un contributo alla ricostruzione virtuale degli affreschi della Chiesa degli Eremitani in Padova (Italian)},
school = {Department of Pure and Applied Mathematics, University of Padua},
year = {1999}
}

M. Fornasier. Una discussione matematica sulla rappresentazione ed il confronto di immagini a meno di rotazioni. Un contributo allamricostruzione informatica degli affreschi nella Chiesa degli Eremitani in Padova (Italian), Technical report DFPD 99/EI/24. Department of Physics "G. Galilei", University of Padua, 1999.
[BibTeX]

BibTeX:
@techreport{F99b,
author = {Massimo Fornasier},
title = {Una discussione matematica sulla rappresentazione ed il confronto di immagini a meno di rotazioni. Un contributo allamricostruzione informatica degli affreschi nella Chiesa degli Eremitani in Padova (Italian)},
school = {Department of Physics "G. Galilei", University of Padua},
year = {1999},
number = {DFPD 99/EI/24},
note = {Technical report}
}

Books 
Fractal Functions, Fractal Surfaces, and Wavelets, 2nd edition, P. R. Massopust, Academic Press, San Diego, pp.426, 2016.
[BibTeX]

BibTeX:
@book{Massopust2016,
title = {Fractal Functions, Fractal Surfaces, and Wavelets},
publisher = {Academic Press; 2nd edition},
year = {2016},
author = {Peter R Massopust},
pages = {426+xix}
owner = {christian},
timestamp = {2016.10.12},
}

Theoretical foundations and numerical methods for sparse recovery, M. Fornasier (ed.), Radon Series on Computational and Applied Mathematics, 9, Walter de Gruyter, Berlin, pp. x+340, 2010.
[BibTeX]

BibTeX:
@book{MR2761798,,
editor = {Fornasier, Massimo},
title = {Theoretical foundations and numerical methods for sparse recovery},
publisher = {Walter de Gruyter, Berlin},
year = {2010},
volume = {9},
pages = {x+340},
doi = {10.1515/9783110226157}
}


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