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Optimization and Data Analysis - Oberseminar

Upcoming Talk

No more talks this semester.

Contacts

Person E-Mail Office
Massimo Fornasier massimo.fornasierematma.tum.de MI 02.10.058
Felix Krahmer felix.krahmeremattum.de MI 02.10.039
Peter Massopust massopustematma.tum.de MI 02.08.040
Carlos Améndola Cerón carlos.amendolaemattum.de MI 02.08.038
Michael Rauchensteiner michael.rauchensteinerematma.tum.de MI 02.10.052

All Scheduled Talks

Mon, 11.05.2020 14:00 - 15:30
Speaker Oleh Melnyk
Title Well conditioned ptychograpic imaging via lost subspace completion
Abstract Ptychography, a special case of the phase retrieval problem, is a popular method in modern imaging. Its measurements are based on the shifts of a locally supported window function. In general, direct recovery of an object from such measurements is known to be an ill-posed problem. Although for some windows the conditioning can be controlled, for a number of important cases it is not possible, for instance for Gaussian windows. In this paper we develop a subspace completion algorithm, which enables stable reconstruction for a much wider choice of windows, including Gaussian windows. The combination with a regularization technique leads to improved conditioning and better noise robustness. This is a joint work with Anton Forstner, Felix Krahmer and Nada Sissouno.
Room Online

Mon, 18.05.2020 14:00 - 15:30
Speaker Claudio Verdun
Title Efficient testing strategies for SARS-CoV-2 (Part I)
Abstract How are tests for SARS-CoV-2 performed? Is it possible to test the whole population? What can be done when the demand for such tests overwhelms the capacity of testing laboratories or there is a shortage of necessary materials to conduct the tests? In this informal series of talks we will show how some ideas developed in the forties can optimize testing strategies which could increase the effectiveness of governmental policies against COVID-19 and hence would help flattening the curve.
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Mon, 25.05.2020 14:00 - 15:30
Speaker Tim Fuchs
Title Efficient testing strategies for SARS-CoV-2 (Part II)
Abstract How are tests for SARS-CoV-2 performed? Is it possible to test the whole population? What can be done when the demand for such tests overwhelms the capacity of testing laboratories or there is a shortage of necessary materials to conduct the tests? In this informal series of talks we will show how some ideas developed in the forties can optimize testing strategies which could increase the effectiveness of governmental policies against COVID-19 and hence would help flattening the curve.
Room Online

Mon, 08.06.2020 14:00 - 15:30
Speaker Massimo Fornasier
Title The Mantegna frescoes in Padua: computer assisted puzzle solving and recolorization (Part I)
Abstract In 1944, near the end of World War II, an allied bombing campaign destroyed the Eremitani church in Padua, Italy. The church was famous among art lovers for its magnificent frescoes, which included a series by the early renaissance painter Andrea Mantegna (1431-1506). Over 88.000 small pieces of painted plaster, of an average area of only 4-5 square centimeters, had been lovingly collected and conserved after the bombing; together, they accounted for less than 80 square meters –only a very small fraction of the area covered by the frescoes originally. From 1992 onwards, art conservation experts attacked the task of cleaning and photographing every piece, sorting them and hoping to reconstruct at least some fragments. The herculean task seemed hopeless –until mathematics came to the rescue. We developed an approach that made it possible, for each small piece of plaster that still showed an element of the design of the fresco, to find where it belonged exactly. The resulting very fragmented and mosaic-like reconstruction of the color scheme of each fresco was then used, via another algorithm, to fill in the color information for the whole fresco.
Room Online

Mon, 15.06.2020 14:00 - 15:30
Speaker Marco Mondelli (IST Austria)
Title Understanding Gradient Descent for Over-parameterized Deep Neural Networks
Abstract Training a neural network is a non-convex problem that exhibits spurious and disconnected local minima. Yet, in practice neural networks with millions of parameters are successfully optimized using gradient descent methods. In this talk, I will give some theoretical insights on why this is possible. First, I will show that the combination of stochastic gradient descent and over-parameterization makes the landscape of deep networks approximately connected and, therefore, more favorable to optimization. Then, I will focus on a special case (two-layer network fitting a convex function) and provide a quantitative convergence result by exploiting the displacement convexity of a related Wasserstein gradient flow. Finally, I will go back to deep networks and show that a single wide layer suffices to guarantee that gradient descent linearly converges to a global optimum. Based on joint work with Adel Javanmard, Andrea Montanari, Quynh Nguyen, and Alexander Shevchenko.
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Mon, 22.06.2020 14:00 - 15:30
Speaker Massimo Fornasier
Title The Mantegna frescoes in Padua: computer assisted puzzle solving and recolorization (Part II)
Abstract In 1944, near the end of World War II, an allied bombing campaign destroyed the Eremitani church in Padua, Italy. The church was famous among art lovers for its magnificent frescoes, which included a series by the early renaissance painter Andrea Mantegna (1431-1506). Over 88.000 small pieces of painted plaster, of an average area of only 4-5 square centimeters, had been lovingly collected and conserved after the bombing; together, they accounted for less than 80 square meters –only a very small fraction of the area covered by the frescoes originally. From 1992 onwards, art conservation experts attacked the task of cleaning and photographing every piece, sorting them and hoping to reconstruct at least some fragments. The herculean task seemed hopeless –until mathematics came to the rescue. We developed an approach that made it possible, for each small piece of plaster that still showed an element of the design of the fresco, to find where it belonged exactly. The resulting very fragmented and mosaic-like reconstruction of the color scheme of each fresco was then used, via another algorithm, to fill in the color information for the whole fresco.
Room Online

Mon, 29.06.2020 14:00 - 15:30
Speaker Bernhard Schmitzer
Title Particle trajectories from dynamic PET via optimal transport regularization
Abstract Positron emission tomography (PET) can measure the distribution of radiolabelled biomarkers in the body. For research and therapy it is desirable to trace small amounts of markers as they flow through the patient. Unfortunately conventional PET image reconstruction techniques break down in this regime due to particle motion and low signal intensity. We propose a functional which explicitly models the flow of the biomarker and enforces temporal consistency by regularization with optimal transport.
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Mon, 06.07.2020 14:00 - 15:30
Speaker Olga Graf
Title Sampling and reconstruction beyond Fourier domain
Abstract The Special Affine Fourier Transform or the SAFT generalizes a number of well-known unitary transformations that are used in signal processing and optics (e.g., Fourier, Fractional Fourier, Fresnel). In this talk, we will use notion of SAFT-bandlimited functions and review key results from extension of Shannon's sampling theory based on the convolution structure tailored for the SAFT domain. We’ll also introduce a new signal representation for the Fractional Fourier (FrFt) domain, namely, one-bit sampling and reconstruction method in the FrFT domain, by employing Sigma-Delta modulation.
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Mon, 13.07.2020 14:00 - 15:30
Speaker Carlos Améndola
Title Structure Learning for Cyclic Linear Causal Models
Abstract We consider the problem of structure learning for linear causal models based on observational data. We treat models given by possibly cyclic mixed graphs, which allow for feedback loops and effects of latent confounders. Generalizing related work on bow-free acyclic graphs, we assume that the underlying graph is simple. This entails that any two observed variables can be related through at most one direct causal effect and that (confounding-induced) correlation between error terms in structural equations occurs only in absence of direct causal effects. We show that, despite new subtleties in the cyclic case, the considered simple cyclic models are of expected dimension and that a previously considered criterion for distributional equivalence of bow-free acyclic graphs has an analogue in the cyclic case. Our result on model dimension justifies in particular score-based methods for structure learning of linear Gaussian mixed graph models, which we implement via greedy search. This is joint work with Philipp Dettling, Mathias Drton, Federica Onori and Jun Wu.
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Mon, 20.07.2020 14:00 - 15:30
Speaker Michael Perlmutter (Michigan State University)
Title Phase Retrieval from Continuous Spectrogram Measurements via Wigner Deconvolution and Angular Synchronization
Abstract We will discuss phase retrieval from locally supported STFT magnitude measurements of a vector $x$ based on a four-step approach: First, we carefully discetize a continuous function $f$ and represenst it by a vector $$. Then, we use a discrete, aliased Wigner distribution deconvolution approach is used to solve for a portion of the lifted rank-one signal $xx^*$. Next, an angular synchronization approach is used to recover x from the known portion of $xx^*$, and finally, we construct a $f$ as a trigonometric polynomial based off of the discrete Fourier transform of $x$. This algorithm provably converges to the exact solution in the noiseless case and is robust to arbitrary additive noise. We will also discuss lower bounds for the Lipschitz continuity of these measurements based off of the size of the support of our measurement masks. These lower bounds are independent of our reconstruction algorithm and give insight into the best possible performance of any such method.
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Mon, 27.07.2020 14:00 - 15:30
Speaker Frank Filbir
Title Approximation of the Finite Hilbert Transform and its Relation to Phase Retrieval Problem
Abstract In this talk I will show how the finite Hilbert transform is related to the problem of phase retrieval of a univariate signal. I will discuss an algorithm for computing the Hilbert transform of a signal based on approximation by Bernstein polynomials. This allows to calculate the Hilbert transform from samples of the signal at equidistant nodes. The talk is based on joint work with Donatella Occorsio and Woula Themistoclakis.
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