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Submitted Preprints

C. Kümmerle and J. Sigl. Harmonic Mean Iteratively Reweighted Least Squares for Low-Rank Matrix Recovery, March 2017.
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 (HM-IRLS), optimizes a non-convex Schatten-p quasi-norm penalization to promote low-rankness and carries three major strengths, in particular for the matrix completion setting. First, the algorithm converges globally to the low-rank matrix for relevant, interesting cases, for which any other (non-)convex state-of-the-art optimization approach fails the recovery. Secondly, HM-IRLS 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, HM-IRLS exhibits a locally superlinear rate of convergence (of order 2-p) 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:
@unpublished{KS17,
  author = {Kümmerle, C. and Sigl, J.},
  title = {Harmonic Mean Iteratively Reweighted Least Squares for Low-Rank Matrix Recovery},
  year = {2017},
  url = {https://arxiv.org/abs/1703.05038}
}
T. Hudson and M. Morandotti. Properties of screw dislocation dynamics: time estimates on boundary and interior collisions, March 2017.
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 two-dimensional 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:
@unpublished{HM17,
  author = {Hudson, T. and Morandotti, M.},
  title = {Properties of screw dislocation dynamics: time estimates on boundary and interior collisions},
  year = {2017},
  url = {https://arxiv.org/abs/1703.02474}
}
M. Morandotti. Structured Deformations of Continua: Theory and Applications, February 2017.
BibTeX:
@unpublished{Morandotti17,
  author = {Morandotti, M.},
  title = {Structured Deformations of Continua: Theory and Applications},
  year = {2017},
  url = {https://arxiv.org/abs/1702.02105}
}
J.-M. Feng, F. Krahmer and R. Saab. Quantized Compressed Sensing for Partial Random Circulant Matrices, February 2017.
Abstract
We provide the first analysis of a non-trivial 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 one-bit, Sigma-Delta 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 Sigma-Delta 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 non-quantization 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}
}
G. Albi, M. Fornasier and D. Kalise. A Boltzmann approach to mean-field sparse feedback control, November 2016.
BibTeX:
@Unpublished{AFK16,
  author    = {Giacomo Albi and Massimo Fornasier and Dante Kalise},
  title     = {A Boltzmann approach to mean-field 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
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 high-dimensional 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 (lower-dimensional) linear subspaces and the noise is sub-gaussian. 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 no-flux boundary conditions and sharp sensing zones, October 2016.
BibTeX:
@unpublished{ChoiSalem16,
  author = {Y.-P. Choi and S. Salem},
  title = {Propagation of chaos for aggregation equations with no-flux boundary conditions and sharp sensing zones},
  year = {2016},
  url = {https://arxiv.org/pdf/1610.03261v1.pdf}
}
M. F. Barnsley, M. Hegland and P. Massopust. Self-referential functions, October 2016.
BibTeX:
@unpublished{BHM6,
  author = {Barnsley, Michael F., Hegland, Markus, and Massopust, Peter},
  title = {Self-referential functions},
  year = {2016},
  url = {http://arxiv.org/abs/1610.01369}
}
J. A. Carrillo, Y.-P. Choi, P. B. Mucha, and J. Peszek. Sharp conditions to avoid collisions in singular Cucker-Smale interactions, September 2016.
BibTeX:
@unpublished{CCMP16,
  author = {J. A. Carrillo, Y.-P. Choi, P. B. Mucha, and J. Peszek},
  title = {Sharp conditions to avoid collisions in singular Cucker-Smale interactions},
  year = {2016},
  url = {http://arxiv.org/pdf/1609.03447v1.pdf}
}
J.A. Hogan and P. Massopust. Quaternionic B-Splines, August 2016.
BibTeX:
@unpublished{HM16,
  author = {Hogan, Jeffrey A. and Massopust, Peter},
  title = {Quaternionic B-Splines},
  year = {2016},
  url = {http://arxiv.org/abs/1608.08428}
}
Y.-P. Choi and J. Haskovec. Cucker-Smale model with normalized communication weights and time delay, August 2016.
BibTeX:
@unpublished{CH16,
  author = {Y.-P. Choi and J. Haskovec},
  title = {Cucker-Smale model with normalized communication weights and time delay},
  year = {2016},
  url = {http://arxiv.org/pdf/1608.06747v1.pdf}
}
G. Albi, Y.-P. Choi, M. Fornasier and D. Kalise. Mean Field Control Hierarchy, August 2016.
BibTeX:
@unpublished{ACFK16,
  author = {Giacomo Albi and Young-Pil Choi and Massimo Fornasier and Dante Kalise},
  title = {Mean Field Control Hierarchy},
  year = {2016}
}
M. Bongini and M. Fornasier. Sparse control of multiagent systems, 2016.
BibTeX:
@unpublished{bongini16sparsereview,
  author = {Bongini, M. and Fornasier, M.},
  title = {Sparse control of multiagent systems},
  year = {2016},
  note = {Submitted}
}
Y.-P. Choi. Finite-time blow-up phenomena of Vlasov/Navier-Stokes equations and related systems, July 2016.
BibTeX:
@unpublished{CYP16_3,
  author = {Y.-P. Choi},
  title = {Finite-time blow-up phenomena of Vlasov/Navier-Stokes equations and related systems},
  year = {2016},
  url = {http://arxiv.org/pdf/1606.07158v1.pdf}
}
M. Fornasier. Learning and sparse control of multiagent systems, In Proc. 7thECM, pp. 1-31, 2016.
BibTeX:
@inproceedings{F7thECM,
  author = {Massimo Fornasier},
  title = {Learning and sparse control of multiagent systems},
  booktitle = {Proc. 7thECM},
  year = {2016},
  pages = {1--31}
}
B. Bringmann, D. Cremers, F. Krahmer and M. Moeller. The Homotopy Method Revisited: Computing Solution Paths of $ell1$-Regularized Problems, April 2016.
BibTeX:
@unpublished{2016arXiv160500071B,
  author = {Bringmann, B. and Cremers, D. and Krahmer, F. and Moeller, M.},
  title = {The Homotopy Method Revisited: Computing Solution Paths of $ell1$-Regularized Problems},
  year = {2016},
  url = {http://arxiv.org/abs/1605.00071}
}
G. Albi, L. Pareschi and M. Zanella. Opinion dynamics over complex networks: kinetic modeling and numerical methods, April 2016.
BibTeX:
@unpublished{APZ16,
  author = {Albi, Giacomo and Pareschi, Lorenzo and Zanella, Mattia},
  title = {Opinion dynamics over complex networks: kinetic modeling and numerical methods},
  year = {2016},
  url = {http://arxiv.org/abs/1604.00421}
}
F. Krahmer and Y. Liu. Phase Retrieval Without Small-Ball Probability Assumptions, April 2016.
BibTeX:
@unpublished{KL16,
  author = {Felix Krahmer and Yi-Kai Liu},
  title = {Phase Retrieval Without Small-Ball Probability Assumptions},
  year = {2016},
  url = {http://arxiv.org/abs/1604.07281}
}
G. Albi and L. Pareschi. Selective model-predictive control for flocking systems, March 2016.
BibTeX:
@unpublished{2016arXiv160305012A,
  author = {Albi, Giacomo and Pareschi, Lorenzo},
  title = {Selective model-predictive control for flocking systems},
  year = {2016},
  url = {http://arxiv.org/abs/1603.05012}
}
O. Christensen, B. Forster and P. Massopust. Fractional and Complex Pseudo-Splines and the Construction of Parseval Frames, February 2016.
BibTeX:
@unpublished{2016arXiv160208580C,
  author = {Christensen, O. and Forster, B. and Massopust, P.},
  title = {Fractional and Complex Pseudo-Splines and the Construction of Parseval Frames},
  year = {2016},
  url = {http://arxiv.org/abs/1602.08580}
}
M. Bongini, M. Fornasier, M. Hansen and M. Maggioni. Inferring Interaction Rules from Observations of Evolutive Systems I: The Variational Approach, January 2016.
BibTeX:
@unpublished{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},
  year = {2016},
  url = {http://arxiv.org/abs/1602.00342}
}
M. Eller and M. Fornasier. Rotation Invariance in Exemplar-based Image Inpainting, Radon Series on Computational and Applied Mathematics, 2015.
BibTeX:
@incollection{EF_Chapter,
  author = {M. Eller and M. Fornasier},
  title = {Rotation Invariance in Exemplar-based Image Inpainting},
  publisher = {Radon Series on Computational and Applied Mathematics},
  year = {2015}
}
G. Albi, L. Pareschi and M. Zanella. On the optimal control of opinion dynamics on evolving networks, October 2015.
BibTeX:
@unpublished{2015arXiv151100145A,
  author = {Albi, G. and Pareschi, L. and Zanella, M.},
  title = {On the optimal control of opinion dynamics on evolving networks},
  year = {2015},
  url = {http://arxiv.org/abs/1603.05012}
}
M. Bongini, M. Fornasier, F. Rossi and F. Solombrino. Mean-Field Pontryagin Maximum Principle, April 2015.
BibTeX:
@unpublished{BFRS15,
  author = {Bongini, M. and Fornasier, M. and Rossi, F. and Solombrino, F. },
  title = {Mean-Field 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:
@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 Cucker-Smale collective behavior models, 2013.
BibTeX:
@unpublished{FV13,
  author = {Fornasier, Massimo and Vecil, Francesco},
  title = {Numerical analysis on Cucker-Smale collective behavior models},
  year = {2013}
}
M. Ehler and F. Filbir. Metric entropy, n-widths, and sampling of functions on manifolds, November 2013.
BibTeX:
@unpublished{EF13,
  author = {Ehler, M. and Filbir, F.},
  title = {Metric entropy, n-widths, and sampling of functions on manifolds},
  year = {2013},
  url = {https://arxiv.org/abs/1311.1393}
}

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Refereed Journal Articles

to appear

P. Massopust. Local Fractal Interpolation On Unbounded Domains, Proc. Edinburgh Math. Soc., to appear.
BibTeX:
@article{M15,
  author = {Massopust, P.},
  title = {Local Fractal Interpolation On Unbounded Domains},
  journal = {Proc. Edinburgh Math. Soc.},
  year = {to appear},
  url = {https://arxiv.org/abs/1508.03198}
}
M. Bongini and G. Buttazzo. Optimal Control Problems in Transport Dynamics, Math. Mod. Meth. Appl. Sci.:1-30, to appear.
BibTeX:
@article{BB16,
  author = {Bongini, Mattia and Buttazzo, Giuseppe},
  title = {Optimal Control Problems in Transport Dynamics},
  journal = {Math. Mod. Meth. Appl. Sci.},
  year = {to appear},
  pages = {1--30},
  url = {https://arxiv.org/abs/1609.07323}
}
J.A. Carrillo, Y.-P. Choi, M. Hauray and S. Salem. Mean-field limit for collective behavior models with sharp sensitivity regions, J. Eur. Math. Soc.:1-32, to appear.
BibTeX:
@article{2015arXiv151002315C,
  author = {Carrillo, J. A. and Choi, Y.-P. and Hauray, M. and Salem, S.},
  title = {Mean-field limit for collective behavior models with sharp sensitivity regions},
  journal = {J. Eur. Math. Soc.},
  year = {to appear},
  pages = {1--32},
  url = {http://arxiv.org/pdf/1510.02315v2.pdf}
}
P.R. Massopust and P.J. Van Fleet. Fractional Cone Splines and Hex Splines, Rocky Mountain J. Math., to appear.
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 s-dimensional meshes and include as special cases the three-directional box splines tearticle:condat and hex splines tearticle: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 B-splines defined in tearticle:ub,article:fbu and investigated in, e.g., tearticle:fm,article:mf. Explicit time domain representations are derived for these splines on 3-directional 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{MF15,
  author = {Massopust, Peter R and Van Fleet, Patrick J},
  title = {Fractional Cone Splines and Hex Splines},
  journal = {Rocky Mountain J. Math.},
  year = {to appear},
  url = {http://arxiv.org/abs/1504.00546}
}

2017

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):20-37, 2017.
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 = {20-37},
  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):423-438, 2017.
Abstract
We consider the problem of estimating the curvature profile along the boundaries of digital objects in segmented black-and-white 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 = {423--438},
  doi = {10.1007/s10851-016-0685-1}
}
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):231-290, 2017.
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 discrete-to-continuum 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 = {231-290},
  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
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 fine-scale 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 non-zero. 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
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 Self-Organizing Agents Leaving Unknown Environments, SIAM J. Appl. Math., 76(4):1683-1710, 2016.
BibTeX:
@article{ABCK16,
  author = {Giacomo Albi and Mattia Bongini and Emiliano Cristiani and Dante Kalise},
  title = {Invisible Control of Self-Organizing Agents Leaving Unknown Environments},
  journal = {SIAM J. Appl. Math.},
  year = {2016},
  volume = {76},
  number = {4},
  pages = {1683-1710},
  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):755-792, 2016.
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 p-norm, 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 non-quadratic possibly non-convex and non-smooth 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, low-rank matrix optimization, and for the solution of PDE involving p-Laplacians) 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 = {755--792},
  doi = {10.1007/s10589-016-9829-x}
}
J.A. Carrillo, Y.-P. Choi and E. Zatorska. On the pressureless damped Euler-Poisson equations with quadratic confinement: Critical thresholds and large-time behavior, Math. Mod. Meth. Appl. Sci., 26(12): 2311-2340, 2016.
BibTeX:
@article{CCZ16,
  author = {Carrillo, José A. and Choi, Young-Pil and Zatorska, Ewelina},
  title = {On the pressureless damped Euler-Poisson equations with quadratic confinement: Critical thresholds and large-time behavior},
  journal = {Math. Mod. Meth. Appl. Sci.},
  year = {2016},
  volume = {26},
  number = {12},
  pages = {2311--2340},
  url = {http://arxiv.org/abs/1604.05229},
  doi = {10.1142/S0218202516500548}
}
Y.-P. Choi. Global classical solutions and large-time behavior of the two-phase fluid model, SIAM J. Math. Anal., 48(5):3090-3122, 2016.
BibTeX:
@article{CYP16_2,
  author = {Choi, Y.-P.},
  title = {Global classical solutions and large-time behavior of the two-phase fluid model},
  journal = {SIAM J. Math. Anal.},
  year = {2016},
  volume = {48},
  number = {5},
  pages = {3090--3122},
  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):209-231, 2016.
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 = {209--231},
  url = {http://arxiv.org/abs/1405.1332v5},
  doi = {10.1007/s00025-015-0475-x}
}
M. Fornasier, S. Peter, H. Rauhut and S. Worm. Conjugate gradient acceleration of iteratively re-weighted least squares methods, Computational Optimization and Applications, 65(1):205-259, 2016.
Abstract
Iteratively re-weighted least squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, 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 non-convex and non-smooth 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 speed-up the numerical solution of the quadratic subproblems, in particular, when fast matrix-vector 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 Soft-Thresholding 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 re-weighted least squares methods},
  journal = {Computational Optimization and Applications},
  year = {2016},
  volume = {65},
  number = {1},
  pages = {205--259},
  url = {http://arxiv.org/abs/1509.04063},
  doi = {10.1007/s10589-016-9839-8}
}
M. Fornasier and J.-C. Hütter. Consistency of Probability Measure Quantization by Means of Power Repulsion--Attraction Potentials, J. Fourier Anal. Appl., 22(3):694-749, 2016.
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 Γ-converge 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 semi-definite 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 Γ-convergence. 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, Jan-Christian},
  title = {Consistency of Probability Measure Quantization by Means of Power Repulsion--Attraction Potentials},
  journal = {J. Fourier Anal. Appl.},
  year = {2016},
  volume = {22},
  number = {3},
  pages = {694--749},
  doi = {10.1007/s00041-015-9432-z}
}
Y.-P. Choi. Large-time behavior for the Vlasov/compressible Navier-Stokes equations, J. Math. Phys., 57(7):071501, 2016.
BibTeX:
@article{CYP16,
  author = {Y.-P. Choi},
  title = {Large-time behavior for the Vlasov/compressible Navier-Stokes 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 Vlasov-Fokker-Planck equation with local alignment forces, Nonlinearity, 29(7):1887-1916, 2016.
BibTeX:
@article{C16,
  author = {Y.-P. Choi},
  title = {Global classical solutions of the Vlasov-Fokker-Planck equation with local alignment forces},
  journal = {Nonlinearity},
  year = {2016},
   volume = {29},
  number = {7},
  pages = {1887--1916},
  url = {http://iopscience.iop.org/article/10.1088/0951-7715/29/7/1887},
  doi = {10.1088/0951-7715/29/7/1887}
}

Y.-P. Choi and B. Kwon. The Cauchy problem for the pressureless Euler/isentropic Navier-Stokes equations, Journal of Differential Equations, 261(1):654-711, 2016.
BibTeX:
@article{CK16,
  author = {Y.-P. Choi and B. Kwon},
  title = {The Cauchy problem for the pressureless Euler/isentropic Navier-Stokes equations},
  journal = {Journal of Differential Equations},
  year = {2016},
  volume = {261},
  number = {1},
  pages = {654--711},
  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):1-18, 2016.
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 information-flow 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 box-covering dimensions. However, box-covering dimensions are only applicable to fractal networks. The construction of these network-dimensions 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 = {1--18},
  doi = {10.1186/s12859-016-0933-9}
}
A. Israel, F. Krahmer and R. Ward. An arithmetic-geometric mean inequality for products of three matrices, Linear Algebra and its Applications, 488:1-12, 2016.
BibTeX:
@article{IKW14,
  author = {Israel, Arie and Krahmer, Felix and Ward, Rachel},
  title = {An arithmetic-geometric mean inequality for products of three matrices},
  journal = {Linear Algebra and its Applications},
  year = {2016},
  volume = {488},
  pages = {1--12},
  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 p-Poisson equation, Nonlinear Anal., 130:298-329, 2016.
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 p-Poisson equation},
  journal = {Nonlinear Anal.},
  year = {2016},
  volume = {130},
  pages = {298--329},
  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):383-417, 2016.
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 = {383--417},
  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):185-206, 2016.
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 = {185--206},
  doi = {10.1142/S0219530515400059}
}
M. Bongini, A. Ciabattoni and F. Montagna. Proof search and Co-NP completeness for many-valued logics, Fuzzy Sets and Systems, 292:130-149, 2016.
BibTeX:
@article{MR3471212,
  author = {Bongini, Mattia and Ciabattoni, Agata and Montagna, Franco},
  title = {Proof search and Co-NP completeness for many-valued logics},
  journal = {Fuzzy Sets and Systems},
  year = {2016},
  volume = {292},
  pages = {130--149},
  doi = {10.1016/j.fss.2015.02.016}
}
P.R. Massopust. On local fractal functions in Besov and Triebel-Lizorkin spaces., J. Math. Anal. Appl., 436(1):393-407, Elsevier, San Diego, CA, 2016.
BibTeX:
@article{zbMATH06536912,
  author = {Peter R. Massopust},
  title = {On local fractal functions in Besov and Triebel-Lizorkin spaces.},
  journal = {J. Math. Anal. Appl.},
  publisher = {Elsevier, San Diego, CA},
  year = {2016},
  volume = {436},
  number = {1},
  pages = {393--407},
  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):521-564, 2015.
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 = {521-564},
  doi = {10.1142/S0218202515400059}
}
M. Iwen and F. Krahmer. Fast Subspace Approximation via Greedy Least-Squares, Constr. Approx., 42(2):281-301, 2015.
BibTeX:
@article{IK13,
  author = {Iwen, M. and Krahmer, F.},
  title = {Fast Subspace Approximation via Greedy Least-Squares},
  journal = {Constr. Approx.},
  year = {2015},
  volume = {42},
  number = {2},
  pages = {281--301},
  doi = {10.1007/s00365-014-9273-z}
}
F. Krahmer, D. Needell and R. Ward. Compressive Sensing with Redundant Dictionaries and Structured Measurements, SIAM J. Math. Anal., 47(6):4606-4629, 2015.
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 = {4606--4629},
  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):561-589, 2015.
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 = {561--589},
  doi = {10.1007/s10208-014-9224-x}
}
C.K. Chui, F. Filbir and H.N. Mhaskar. Representation of functions on big data: graphs and trees, Appl. Comput. Harmon. Anal., 38(3):489-509, 2015.
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 = {489--509},
  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):1407-1429, 2015.
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 = {1407--1429},
  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:
@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):B633-B659, 2015.
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 = {B633--B659},
  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 Ill-Posed Probl., 23(4):393-414, 2015.
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 Ill-Posed Probl.},
  year = {2015},
  volume = {23},
  number = {4},
  pages = {393--414},
  doi = {10.1515/jiip-2014-0031}
}
M. Bongini, M. Fornasier and D. Kalise. (Un)conditional consensus emergence under perturbed and decentralized feedback controls, Discrete Contin. Dyn. Syst., 35(9):4071-4094, 2015.
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 = {4071--4094},
  doi = {10.3934/dcds.2015.35.4071}
}
S. Peter, M. Artina and M. Fornasier. Damping noise-folding and enhanced support recovery in compressed sensing, IEEE Trans. Signal Process., 63(22):5990-6002, 2015.
BibTeX:
@article{MR3411372,
  author = {Peter, Steffen and Artina, Marco and Fornasier, Massimo},
  title = {Damping noise-folding and enhanced support recovery in compressed sensing},
  journal = {IEEE Trans. Signal Process.},
  year = {2015},
  volume = {63},
  number = {22},
  pages = {5990--6002},
  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):647-697, 2015.
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 = {647--697},
  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):2475-2494, 2015.
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 = {2475--2494},
  url = {http://arxiv.org/abs/1501.04305},
  doi = {10.1137/141001408}
}

2014

J. Feng and F. Krahmer. An RIP approach to Sigma-Delta quantization for compressed sensing, IEEE Signal Process. Lett., 21(11):1351-1355, 2014.
BibTeX:
@article{FK14,
  author = {Feng, J. and Krahmer, F},
  title = {An RIP approach to Sigma-Delta quantization for compressed sensing},
  journal = {IEEE Signal Process. Lett.},
  year = {2014},
  volume = {21},
  number = {11},
  pages = {1351--1355},
  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):229-266, 2014.
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 = {229--266},
  url = {http://arxiv.org/abs/1310.2267},
  doi = {10.1007/s00041-014-9361-2}
}
F. Krahmer, G. Kutyniok and J. Lemvig. Sparse Matrices in Frame Theory, Computational Statistics, 29:547-568, 2014.
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 = {547--568},
  doi = {10.1007/s00180-013-0446-1}
}
F.. Krahmer, S.. Mendelson and H.. Rauhut. Suprema of Chaos Processes and the Restricted Isometry Property, Comm. Pure Appl. Math., 67(11):1877-1904, 2014.
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 = {1877-1904},
  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 Kohn-Nirenberg symbols, Constr. Approx., 39(3):541-572, 2014.
BibTeX:
@article{KP13,
  author = {Krahmer, F. and Pfander, G.},
  title = {Local sampling and approximation of operators with bandlimited Kohn-Nirenberg symbols},
  journal = {Constr. Approx.},
  year = {2014},
  volume = {39},
  number = {3},
  pages = {541-572},
  doi = {10.1007/s00365-014-9228-4}
}
F.. Krahmer and H.. Rauhut. Structured random measurements in signal processing, GAMM-Mitteilungen, 37(2):217-238, 2014.
BibTeX:
@inproceedings{KR14,
  author = {Krahmer, F. and Rauhut, H.},
  title = {Structured random measurements in signal processing},
  journal = {GAMM-Mitteilungen},
  year = {2014},
  volume = {37},
  number = {2},
  pages = {217--238},
  doi = {10.1002/gamm.201410010}
}
F. Krahmer, R. Saab and Ö. Yilmaz. Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing, Inform. Inference, 3(1):40-58, 2014.
BibTeX:
@article{KSY13,
  author = {Krahmer, F. and Saab, R. and Yilmaz, Ö.},
  title = {Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing},
  journal = {Inform. Inference},
  year = {2014},
  volume = {3},
  number = {1},
  pages = {40-58},
  doi = {10.1093/imaiai/iat007}
}
F. Krahmer and R. Ward. Stable and robust sampling strategies for compressive imaging, IEEE Trans. Image Proc., 23(2):612-622, 2014.
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 = {612--622},
  doi = {10.1109/TIP.2013.2288004}
}
B. Scharf. Wavelet decomposition techniques and Hardy inequalities for function spaces on cubes, J. Approx. Theory, 178:41-63, 2014.
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 = {41--63},
  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):1-31, 2014.
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 = {1--31},
  doi = {10.3934/nhm.2014.9.1}
}
M. Ehler, M. Fornasier and J. Sigl. Quasi-linear compressed sensing, Multiscale Model. Simul., 12(2):725-754, 2014.
BibTeX:
@article{MR3213786,
  author = {Ehler, Martin and Fornasier, Massimo and Sigl, Juliane},
  title = {Quasi-linear compressed sensing},
  journal = {Multiscale Model. Simul.},
  year = {2014},
  volume = {12},
  number = {2},
  pages = {725--754},
  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):794-818, 2014.
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 = {794--818},
  url = {http://arxiv.org/abs/1304.5459},
  doi = {10.1137/13091779X}
}
M. Ehler and F. Filbir. varepsilon-coverings of Hölder-Zygmund type spaces on data-defined manifolds, Abstr. Appl. Anal.:Art. ID 402918, 6, 2014.
BibTeX:
@article{MR3226192,
  author = {Ehler, Martin and Filbir, Frank},
  title = {varepsilon-coverings of Hölder-Zygmund type spaces on data-defined 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):1770-1794, 2014.
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 = {1770--1794},
  doi = {10.1137/130930248}
}
M. Fornasier and F. Solombrino. Mean-field optimal control, ESAIM Control Optim. Calc. Var., 20(4):1123-1152, 2014.
BibTeX:
@article{MR3264236,
  author = {Fornasier, Massimo and Solombrino, Francesco},
  title = {Mean-field optimal control},
  journal = {ESAIM Control Optim. Calc. Var.},
  year = {2014},
  volume = {20},
  number = {4},
  pages = {1123--1152},
  doi = {10.1051/cocv/2014009}
}
G. Albi, M. Herty, C. Jörres and L. Pareschi. Asymptotic preserving time-discretization of optimal control problems for the Goldstein-Taylor model, Numer. Methods Partial Differential Equations, 30(6):1770-1784, 2014.
BibTeX:
@article{MR3267352,
  author = {Albi, Giacomo and Herty, Michael and Jörres, Christian and Pareschi, Lorenzo},
  title = {Asymptotic preserving time-discretization of optimal control problems for the Goldstein-Taylor model},
  journal = {Numer. Methods Partial Differential Equations},
  year = {2014},
  volume = {30},
  number = {6},
  pages = {1770--1784},
  url = {http://arxiv.org/pdf/1307.8303v2.pdf},
  doi = {10.1002/num.21877}
}
M. Fornasier, B. Piccoli and F. Rossi. Mean-field sparse optimal control, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 372(2028):20130400, 21, 2014.
BibTeX:
@article{MR3268059,
  author = {Fornasier, Massimo and Piccoli, Benedetto and Rossi, Francesco},
  title = {Mean-field 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. Boltzmann-type control of opinion consensus through leaders, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 372(2028):20140138, 18, 2014.
BibTeX:
@article{MR3268062,
  author = {Albi, G. and Pareschi, L. and Zanella, M.},
  title = {Boltzmann-type 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):2722-2742, 2014.
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 = {2722--2742},
  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):3814-3837, 2014.
BibTeX:
@article{MR3280100,
  author = {Di Francesco, Marco and Fornasier, Massimo and Hütter, Jan-Christian 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 = {3814--3837},
  doi = {10.1137/140951497}
}
V. Naumova and S. Peter. Minimization of multi-penalty functionals by alternating iterative thresholding and optimal parameter choices, Inverse Problems, 30(12):125003, 34, 2014.
BibTeX:
@article{MR3291117,
  author = {Naumova, Valeriya and Peter, Steffen},
  title = {Minimization of multi-penalty functionals by alternating iterative thresholding and optimal parameter choices},
  journal = {Inverse Problems},
  year = {2014},
  volume = {30},
  number = {12},
  pages = {125003, 34},
  doi = {10.1088/0266-5611/30/12/125003}
}

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:
@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:
@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 = {10.1088/0266-5611/29/1/015002}
}
M. Fornasier, R. March and F. Solombrino. Existence of minimizers of the Mumford-Shah functional with singular operators and unbounded data, Ann. Mat. Pura Appl. (4), 192(3):361-391, 2013.
BibTeX:
@article{MR3061104,
  author = {Fornasier, Massimo and March, Riccardo and Solombrino, Francesco},
  title = {Existence of minimizers of the Mumford-Shah functional with singular operators and unbounded data},
  journal = {Ann. Mat. Pura Appl. (4)},
  year = {2013},
  volume = {192},
  number = {3},
  pages = {361--391},
  doi = {10.1007/s10231-011-0228-8}
}
M. Artina, M. Fornasier and F. Solombrino. Linearly constrained nonsmooth and nonconvex minimization, SIAM J. Optim., 23(3):1904-1937, 2013.
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 = {1904--1937},
  doi = {10.1137/120869079}
}
M. Caponigro, M. Fornasier, B. Piccoli and E. Trélat. Sparse stabilization and optimal control of the Cucker-Smale model, Math. Control Relat. Fields, 3(4):447-466, 2013.
BibTeX:
@article{MR3110059,
  author = {Caponigro, Marco and Fornasier, Massimo and Piccoli, Benedetto and Trélat, Emmanuel},
  title = {Sparse stabilization and optimal control of the Cucker-Smale model},
  journal = {Math. Control Relat. Fields},
  year = {2013},
  volume = {3},
  number = {4},
  pages = {447--466},
  doi = {10.3934/mcrf.2013.3.447}
}
M. Fornasier, J. Haškovec and G. Steidl. Consistency of variational continuous-domain quantization via kinetic theory, Appl. Anal., 92(6):1283-1298, 2013.
BibTeX:
@article{MR3197935,
  author = {Fornasier, Massimo and Haškovec, Jan and Steidl, Gabriele},
  title = {Consistency of variational continuous-domain quantization via kinetic theory},
  journal = {Appl. Anal.},
  year = {2013},
  volume = {92},
  number = {6},
  pages = {1283--1298},
  doi = {10.1080/00036811.2012.671299}
}

2012

M. Burr and F. Krahmer. SqFreeEVAL: An (almost) optimal real-root isolation algorithm, Journal of Symbolic Computation, 47(2):153-166, 2012.
BibTeX:
@article{BK11,
  author = {Burr, M. and Krahmer, F.},
  title = {SqFreeEVAL: An (almost) optimal real-root isolation algorithm},
  journal = {Journal of Symbolic Computation},
  year = {2012},
  volume = {47},
  number = {2},
  pages = {153--166},
  doi = {10.1016/j.jsc.2011.08.022}
}
F. Krahmer, R. Saab and R. Ward. Root-exponential accuracy for coarse quantization of finite frame expansions, IEEE J. Inf. Theo., 58(2):1069-1079, 2012.
BibTeX:
@article{KSW12,
  author = {Krahmer, F. and Saab, R. and Ward, R.},
  title = {Root-exponential accuracy for coarse quantization of finite frame expansions},
  journal = {IEEE J. Inf. Theo.},
  year = {2012},
  volume = {58},
  number = {2},
  pages = {1069--1079},
  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):131-138, 2012.
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 = {131--138},
  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):419-446, 2012.
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 = {419--446},
  doi = {10.1090/S0025-5718-2011-02507-X}
}
M. Fornasier, K. Schnass and J. Vybiral. Learning functions of few arbitrary linear parameters in high dimensions, Found. Comput. Math., 12(2):229-262, 2012.
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 = {229--262},
  doi = {10.1007/s10208-012-9115-y}
}
M. Ehler, F. Filbir and H.N. Mhaskar. Locally learning biomedical data using diffusion frames, J. Comput. Biol., 19(11):1251-1264, 2012.
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 = {1251--1264},
  doi = {10.1089/cmb.2012.0187}
}
M. Fornasier, Y. Kim, A. Langer and C.-B. Schönlieb. Wavelet decomposition method for L_2/TV-image deblurring, SIAM J. Imaging Sci., 5(3):857-885, 2012.
BibTeX:
@article{MR3022181,
  author = {Fornasier, M. and Kim, Y. and Langer, A. and Schönlieb, C.-B.},
  title = {Wavelet decomposition method for L_2/TV-image deblurring},
  journal = {SIAM J. Imaging Sci.},
  year = {2012},
  volume = {5},
  number = {3},
  pages = {857--885},
  doi = {10.1137/100819801}
}

2011

P. Casazza, A. Heinecke, F. Krahmer and G. Kutyniok. Optimally sparse frames, IEEE J. Inf. Theo., 57(11):7279-7287, 2011.
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 = {7279--7287},
  doi = {10.1109/TIT.2011.2160521}
}
P. Deift, C.S. Güntürk and F. Krahmer. An Optimal Family of Exponentially Accurate One-Bit Sigma-Delta Quantization Schemes, Comm. Pure Appl. Math., 64(7):883-919, 2011.
BibTeX:
@article{DGK11,
  author = {Percy Deift and C. Sinan Güntürk and Felix Krahmer},
  title = {An Optimal Family of Exponentially Accurate One-Bit Sigma-Delta Quantization Schemes},
  journal = {Comm. Pure Appl. Math.},
  year = {2011},
  volume = {64},
  number = {7},
  pages = {883--919},
  doi = {10.1002/cpa.20367}
}
F. Krahmer and R. Ward. New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property, SIAM J. Math. Anal., 43(3):1269-1281, SIAM, 2011.
BibTeX:
@article{KW11,
  author = {Krahmer, F. and Ward, R.},
  title = {New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property},
  journal = {SIAM J. Math. Anal.},
  publisher = {SIAM},
  year = {2011},
  volume = {43},
  number = {3},
  pages = {1269--1281},
  doi = {10.1137/100810447}
}
M. Fornasier, J. Haskovec and G. Toscani. Fluid dynamic description of flocking via the Povzner-Boltzmann equation, Phys. D, 240(1):21-31, 2011.
BibTeX:
@article{MR2740099,
  author = {Fornasier, Massimo and Haskovec, Jan and Toscani, Giuseppe},
  title = {Fluid dynamic description of flocking via the Povzner-Boltzmann equation},
  journal = {Phys. D},
  year = {2011},
  volume = {240},
  number = {1},
  pages = {21--31},
  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):1727-1764, 2011.
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 = {1727--1764},
  doi = {10.1137/110830617}
}
M. Fornasier, H. Rauhut and R. Ward. Low-rank matrix recovery via iteratively reweighted least squares minimization, SIAM J. Optim., 21(4):1614-1640, 2011.
BibTeX:
@article{MR2869510,
  author = {Fornasier, Massimo and Rauhut, Holger and Ward, Rachel},
  title = {Low-rank matrix recovery via iteratively reweighted least squares minimization},
  journal = {SIAM J. Optim.},
  year = {2011},
  volume = {21},
  number = {4},
  pages = {1614--1640},
  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):153-185, 2010.
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 = {153--185},
  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):1-38, 2010.
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 = {1--38},
  doi = {10.1002/cpa.20303}
}
J.A. Carrillo, M. Fornasier, J. Rosado and G. Toscani. Asymptotic flocking dynamics for the kinetic Cucker-Smale model, SIAM J. Math. Anal., 42(1):218-236, 2010.
BibTeX:
@article{MR2596552,
  author = {Carrillo, J. A. and Fornasier, M. and Rosado, J. and Toscani, G.},
  title = {Asymptotic flocking dynamics for the kinetic Cucker-Smale model},
  journal = {SIAM J. Math. Anal.},
  year = {2010},
  volume = {42},
  number = {1},
  pages = {218--236},
  doi = {10.1137/090757290}
}
M. Fornasier and R. Ward. Iterative thresholding meets free-discontinuity problems, Found. Comput. Math., 10(5):527-567, 2010.
BibTeX:
@article{MR2673428,
  author = {Fornasier, Massimo and Ward, Rachel},
  title = {Iterative thresholding meets free-discontinuity problems},
  journal = {Found. Comput. Math.},
  year = {2010},
  volume = {10},
  number = {5},
  pages = {527--567},
  doi = {10.1007/s10208-010-9071-3}
}
M. Fornasier, A. Langer and C.-B. Schönlieb. A convergent overlapping domain decomposition method for total variation minimization, Numer. Math., 116(4):645-685, 2010.
BibTeX:
@article{MR2721637,
  author = {Fornasier, Massimo and Langer, Andreas and Schönlieb, Carola-Bibiane},
  title = {A convergent overlapping domain decomposition method for total variation minimization},
  journal = {Numer. Math.},
  year = {2010},
  volume = {116},
  number = {4},
  pages = {645--685},
  doi = {10.1007/s00211-010-0314-7}
}
R. Duan, M. Fornasier and G. Toscani. A kinetic flocking model with diffusion, Comm. Math. Phys., 300(1):95-145, 2010.
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 = {95--145},
  doi = {10.1007/s00220-010-1110-z}
}

2009

M. Fornasier, R. Ramlau and G. Teschke. The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem, Adv. Comput. Math., 31(1-3):157-184, 2009.
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 real-life art restoration problem},
  journal = {Adv. Comput. Math.},
  year = {2009},
  volume = {31},
  number = {1-3},
  pages = {157--184},
  doi = {10.1007/s10444-008-9103-6}
}
M. Fornasier and C.-B. Schönlieb. Subspace correction methods for total variation and l_1-minimization, SIAM J. Numer. Anal., 47(5):3397-3428, 2009.
BibTeX:
@article{MR2551200,
  author = {Fornasier, Massimo and Schönlieb, Carola-Bibiane},
  title = {Subspace correction methods for total variation and l_1-minimization},
  journal = {SIAM J. Numer. Anal.},
  year = {2009},
  volume = {47},
  number = {5},
  pages = {3397--3428},
  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):1366-1401, 2009.
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 = {1366--1401},
  doi = {10.1002/num.20407}
}

2008

F. Krahmer, Gö.E. Pfander and P. Rashkov. Uncertainty in time-frequency representations on finite abelian groups and applications, Appl. Comput. Harmon. Anal., 25(2):209-225, 2008.
BibTeX:
@article{KraPfaRa08,
  author = {Krahmer, Felix and Pfander, Götz E. and Rashkov, Peter},
  title = {Uncertainty in time-frequency representations on finite abelian groups and applications},
  journal = {Appl. Comput. Harmon. Anal.},
  year = {2008},
  volume = {25},
  number = {2},
  pages = {209--225},
  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):45-75, 2008.
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 = {45--75},
  doi = {10.1007/s00211-007-0127-5}
}
M. Fornasier and H. Rauhut. Recovery algorithms for vector-valued data with joint sparsity constraints, SIAM J. Numer. Anal., 46(2):577-613, 2008.
BibTeX:
@article{MR2383204,
  author = {Fornasier, Massimo and Rauhut, Holger},
  title = {Recovery algorithms for vector-valued data with joint sparsity constraints},
  journal = {SIAM J. Numer. Anal.},
  year = {2008},
  volume = {46},
  number = {2},
  pages = {577--613},
  doi = {10.1137/0606668909}
}
S. Dahlke, M. Fornasier, H. Rauhut, G. Steidl and G. Teschke. Generalized coorbit theory, Banach frames, and the relation to α-modulation spaces, Proc. Lond. Math. Soc. (3), 96(2):464-506, 2008.
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 α-modulation spaces},
  journal = {Proc. Lond. Math. Soc. (3)},
  year = {2008},
  volume = {96},
  number = {2},
  pages = {464--506},
  doi = {10.1112/plms/pdm051}
}
M. Fornasier and H. Rauhut. Iterative thresholding algorithms, Appl. Comput. Harmon. Anal., 25(2):187-208, 2008.
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 = {187--208},
  doi = {10.1016/j.acha.2007.10.005}
}
M. Fornasier and L. Gori. Sampling theorems on bounded domains, J. Comput. Appl. Math., 221(2):376-385, 2008.
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 = {376--385},
  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):386-395, 2008.
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 = {386--395},
  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(5-6):764-792, 2008.
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 = {5-6},
  pages = {764--792},
  doi = {10.1007/s00041-008-9039-8}
}

2007

M. Fornasier. Banach frames for α-modulation spaces, Appl. Comput. Harmon. Anal., 22(2):157-175, 2007.
BibTeX:
@article{MR2295293,
  author = {Fornasier, Massimo},
  title = {Banach frames for α-modulation spaces},
  journal = {Appl. Comput. Harmon. Anal.},
  year = {2007},
  volume = {22},
  number = {2},
  pages = {157--175},
  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):27-63, 2007.
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 = {27--63},
  doi = {10.1007/s10444-005-7501-6}
}
M. Fornasier and R. March. Restoration of color images by vector valued BV functions and variational calculus, SIAM J. Appl. Math., 68(2):437-460, 2007.
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 = {437--460},
  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):717-740, 2007.
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 = {717--740},
  doi = {10.1093/imanum/drl035}
}
M. Fornasier. Domain decomposition methods for linear inverse problems with sparsity constraints, Inverse Problems, 23(6):2505-2526, 2007.
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 = {2505--2526},
  doi = {10.1088/0266-5611/23/6/014}
}

2006

H.G. Feichtinger and M. Fornasier. Flexible Gabor-wavelet atomic decompositions for L^2-Sobolev spaces, Ann. Mat. Pura Appl. (4), 185(1):105-131, 2006.
BibTeX:
@article{MR2179584,
  author = {Feichtinger, Hans G. and Fornasier, Massimo},
  title = {Flexible Gabor-wavelet atomic decompositions for L^2-Sobolev spaces},
  journal = {Ann. Mat. Pura Appl. (4)},
  year = {2006},
  volume = {185},
  number = {1},
  pages = {105--131},
  doi = {10.1007/s10231-004-0130-8}
}
M. Fornasier. Nonlinear projection recovery in digital inpainting for color image restoration, J. Math. Imaging Vision, 24(3):359-373, 2006.
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 = {359--373},
  doi = {10.1007/s10851-006-4242-1}
}
M. Fornasier. On some stability results of localized atomic decompositions, Rend. Mat. Appl. (7), 26(3-4):315-325, 2006.
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 = {3-4},
  pages = {315--325},
  doi = {http://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2006(3-4)/315-325.pdf}
}

2005

M. Fornasier and D. Toniolo. Fast, robust and efficient 2D pattern recognition for re-assembling fragmented images, Pattern Recognition, 38(11):2074-2087, 2005.
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 re-assembling 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 large-scale 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 re-assembling fragmented images},
  journal = {Pattern Recognition},
  year = {2005},
  volume = {38},
  number = {11},
  pages = {2074--2087},
  doi = {10.1016/j.patcog.2005.03.014}
}
M. Fornasier and K. Gröchenig. Intrinsic localization of frames, Constr. Approx., 22(3):395-415, 2005.
BibTeX:
@article{MR2164142,
  author = {Fornasier, Massimo and Gröchenig, Karlheinz},
  title = {Intrinsic localization of frames},
  journal = {Constr. Approx.},
  year = {2005},
  volume = {22},
  number = {3},
  pages = {395--415},
  doi = {10.1007/s00365-004-0592-3}
}
M. Fornasier and H. Rauhut. Continuous frames, function spaces, and the discretization problem, J. Fourier Anal. Appl., 11(3):245-287, 2005.
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 = {245--287},
  doi = {10.1007/s00041-005-4053-6}
}
M. Morandi Cecchi and M. Fornasier. Fast homogenization algorithm based on asymptotic theory and multiscale schemes, Numer. Algorithms, 40(2):171-186, 2005.
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 = {171--186},
  doi = {10.1007/s11075-005-1530-6}
}

2004

M. Fornasier. Quasi-orthogonal decompositions of structured frames, J. Math. Anal. Appl., 289(1):180-199, 2004.
BibTeX:
@article{MR2020535,
  author = {Fornasier, Massimo},
  title = {Quasi-orthogonal decompositions of structured frames},
  journal = {J. Math. Anal. Appl.},
  year = {2004},
  volume = {289},
  number = {1},
  pages = {180--199},
  doi = {10.1016/j.jmaa.2003.09.041}
}

2003

M. Fornasier. Function spaces inclusions and rate of convergence of Riemann-type sums in numerical integration, Numer. Funct. Anal. Optim., 24(1-2):45-57, 2003.
BibTeX:
@article{MR1978950,
  author = {Fornasier, Massimo},
  title = {Function spaces inclusions and rate of convergence of Riemann-type sums in numerical integration},
  journal = {Numer. Funct. Anal. Optim.},
  year = {2003},
  volume = {24},
  number = {1-2},
  pages = {45--57},
  doi = {10.1081/NFA-120020243}
}

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Conference Papers

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. 970828-970828-8, 2016.
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 ℓ1-norm. 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 = {970828-970828-8},
  doi = {10.1117/12.2209301}
}
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:
@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. 3-10, 2013.
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 = {3--10},
  doi = {10.1007/978-3-642-28021-4_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:
@inproceedings{bretti:inria-00369432,
  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. 337-338, 2009.
BibTeX:
@inproceedings{bridges2009:337,
  author = {Wolfgang Baatz and Massimo Fornasier and Peter A. Markowich and Carola-Bibiane 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 = {337--338},
  note = {Available online at http://archive.bridgesmathart.org/2009/bridges2009-337.html}
}
M. Fornasier. Compressive Algorithms---Adaptive 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 7-9, 2009 Proceedings, Springer Berlin Heidelberg Berlin, Heidelberg, pp. 143-169, 2009.
BibTeX:
@incollection{F09,
  author = {Fornasier, M.},
  editor = {Hancock, Edwin R. and Martin, Ralph R. and Sabin, Malcolm A.},
  title = {Compressive Algorithms---Adaptive Solutions of PDEs and Variational Problems},
  booktitle = {Mathematics of Surfaces XIII: 13th IMA International Conference York, UK, September 7-9, 2009 Proceedings},
  publisher = {Springer Berlin Heidelberg},
  year = {2009},
  pages = {143--169},
  doi = {10.1007/978-3-642-03596-8_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:
@inproceedings{FLS09,
  author = {Massimo Fornasier and Andreas Langer and Carola-Bibiane 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 Re-weighted 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. 26-29, 2008.
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 re-weighted 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 lscr1-minimization, the exponential rate is linear; in adapted versions aimed at lscrtau-minimization 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 Re-weighted 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 = {26-29},
  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. 163-170, 2008.
BibTeX:
@inproceedings{bridges2008:163,
  author = {Wolfgang Baatz, Massimo Fornasier, Peter A. Markowich and and Carola-Bibiane 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 = {163--170},
  note = {Available online at http://archive.bridgesmathart.org/2008/bridges2008-163.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, Springer-Verlag Berlin, Heidelberg, pp. 116-127, 2007.
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 = {Springer-Verlag},
  year = {2007},
  pages = {116--127},
  doi = {10.1007/978-3-540-72823-8_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 16--20, 2005., Weinheim: Wiley-VCH, pp. 619-623, 2005.
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 16--20, 2005.},
  publisher = {Weinheim: Wiley-VCH},
  year = {2005},
  pages = {619--623}
}
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, Mini-Workshop: Wavelets and Frames, 1(1), pp. 479-544, 2004.
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, Mini-Workshop: Wavelets and Frames},
  journal = {Oberwolfach Reports},
  year = {2004},
  volume = {1},
  number = {1},
  pages = {479--544}
}
M. Fornasier. Decompositions of Hilbert spaces: local construction of global frames, In Constructive theory of functions, DARBA, Sofia, pp. 275-281, 2003.
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 = {275--281}
}

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Book Chapters

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.), Birkhäuser-Springer, to appear.
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 = {Birkhäuser-Springer},
  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.), Birkhäuser-Springer, to appear.
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 = {Birkhäuser-Springer},
  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. 205-256, 2015.
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 = {205--256},
  doi = {10.1007/978-1-4939-0790-8_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:
@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 plane-strain conditions, In: New challenges in grid generation and adaptivity for scientific computing, 5, Springer, Cham, pp. 43-67, 2015.
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 plane-strain conditions},
  booktitle = {New challenges in grid generation and adaptivity for scientific computing},
  publisher = {Springer, Cham},
  year = {2015},
  volume = {5},
  pages = {43--67},
  doi = {10.1007/978-3-319-06053-8_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 26--30, 2013, Cham: Springer, pp. 293-301, 2015.
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 26--30, 2013},
  publisher = {Cham: Springer},
  year = {2015},
  pages = {293--301},
  doi = {10.1007/978-3-319-10705-9_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. 93-200, 2010.
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 = {93--200},
  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 socio-economic and life sciences, Birkhäuser Boston, Inc., Boston, MA, pp. 297-336, 2010.
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 socio-economic and life sciences},
  publisher = {Birkhäuser Boston, Inc., Boston, MA},
  year = {2010},
  pages = {297--336},
  doi = {10.1007/978-0-8176-4946-3_12}
}
M. Fornasier. Mathknow: Mathematics, Applied Sciences and Real Life, M. Emmer and A. Quarteroni (ed.), Springer Milan Milano, pp. 217-228, 2009.
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 = {217--228},
  doi = {10.1007/978-88-470-1122-9_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:
@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. 15-23, 2003.
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 = {15--23}
}

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PhD Theses

S. Peter. Algorithms for Robust and Fast Sparse Recovery. Technische Universität München, 2016.
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:
@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 Non-Convex Minimizations and Applications in Fracture Mechanics. Technische Universität München, 2015.
BibTeX:
@phdthesis{ArtinaThesis15,
  author = {Artina, Marco},
  title = {Lagrangian Methods for Constrained Non-Convex 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 Sigma-Delta Modulation: From Improved Exponential Accuracy to Low-Complexity Design. New York University, 2009.
BibTeX:
@phdthesis{KrThesis,
  author = {Felix Krahmer},
  title = {Novel Schemes for Sigma-Delta Modulation: From Improved Exponential Accuracy to Low-Complexity Design},
  school = {New York University},
  year = {2009},
  url = {http://num.math.uni-goettingen.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:
@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:
@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

M. Burr, F. Krahmer and C. Yap. Continuous Amortization: A non-probabilistic adaptive analysis technique, Technical report. Electronic Colloquium on Computational Complexity, 2009.
BibTeX:
@techreport{BuKrYa09,
  author = {Burr, Michael and Krahmer, Felix and Yap, Chee},
  title = {Continuous Amortization: A non-probabilistic 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 time-frequency representations on finite Abelian groups, Technical report. Jacobs University, Bremen, 2007.
BibTeX:
@techreport{KraPfaRa07,
  author = {Krahmer, F. and Pfander, G. and Rashkov, P.},
  title = {Support size conditions for time-frequency 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:
@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:
@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:
@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:
@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:
@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:

@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:

@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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