Harmonic Analysis and Signal Processing Seminar Schedule

Harmonic Analysis and Signal Processing Seminar Schedule

Info: The Harmonic Analysis and Signal Processing seminar is coordinated by C. Sinan Güntürk.
Location and Hour: Warren Weaver Hall (Courant Institute), time and place to be checked on this page or here.

Fall 2010

Date	Time and Place	Speaker and Institution	Title and Abstract
Sep 17	11:30am, WWH 1302	Stephane Mallat, Ecole Polytechnique	Classification by Invariant Scattering (joint with the Applied Mathematics Seminar)
Nov 18	2pm, WWH 317	Franz Luef, UC Berkeley	Gabor Analysis as Noncommutative Geometry Over Noncommutative Tori
Nov 23	3:30pm, WWh 1302	Zuowei Shen, National University of Singapore	Wavelet Frames and Applications (joint with the Applied Mathematics Seminar)

Spring 2010

Date	Time and Place	Speaker and Institution	Title and Abstract
Jan 27	2:00pm, WWH 1314	Luis Daniel Abreu, CMUC, University of Coimbra, Portugal	Gabor and wavelet (super)frames with Hermite and Laguerre functions
Feb 17	2:00pm, WWH 1314	Katya Scheinberg, Columbia University and CIMS	Efficiently recovering second-order models in derivative-free optimization
Feb 24	2:00pm, WWH 1314	William Wu, Stanford University	Discrete Sampling
Mar 3	2:00pm, WWH 1314	Felix Krahmer, Hausdorff Center for Mathematics, University of Bonn	Local Approximation and Quantization of Operators with Bandlimited Kohn-Nirenberg Symbols
Mar 10	2:00pm, WWH 1314	Rachel Ward, CIMS	Sparse Legendre expansions via l1 minimization
Mar 22	11:00am, WWH 202	Joel Tropp, Caltech	Finding Structure with Randomness (Note the special time and location)

Fall 2009

Date	Time and Place	Speaker and Institution	Title and Abstract
Nov 18	3:30pm, WWH 517	Vikram Jandhyala, Associate Professor and Director, Applied Computational Engineering Lab, Dept of Electrical Engineering, University of Washington Seattle Founder and Chairman, Physware Inc.	Open challenges in field-based microelectronics design and verification (joint with Special Applied Mathematics Seminar)

Spring 2009

Date	Time and Place	Speaker and Institution	Title and Abstract
March 6	1:00pm, WWH 1314	Mario A. T. Figueiredo, Instituto de Telecomunicações, Instituto Superior Tecnico, Lisboa, Portugal	Iterative Shrinkage/Thresholding Algorithms: Some History and Recent Developments
March 25	3:30pm, WWH 201	Yoel Shkolnisky, Department of Mathematics Yale University	Reference Free Cryo-EM Structure Determination through Eigenvectors of Sparse Matrices

Fall 2007

Date	Time and Place	Speaker and Institution	Title and Abstract
Oct 30	12:30pm, WWH 1302	Martin Raphan, CIMS and Laboratory for Computational Vision, Center for Neural Science, NYU	Unsupervised Regression for Image Denoising

Spring 2007

Mini Workshop on Sparsity and Approximation
Monday, April 30th 2007

Massimo Fornasier, Princeton University

Iterative Thresholding Algorithms for Inverse Problems with Sparsity Constraints

Abstract. Since the work of Donoho and Johnstone, soft and hard thresholding operators have been extensively studied for denoising of digital signals, mainly in a statistical framework. Usually associated to wavelet or curvelet expansions, thresholding allows to eliminate those coefficients which encode noise components. The assumption is that signals are sparse in origin with respect to such expansions and that the effect of noise is essentially to perturb the sparsity structure by introducing non zero coefficients with relatively small magnitude. While a simple and direct thresholding is used for statistical estimation of the relevant components of an explicitly given signal, and to discard those considered disturbance, the computation of the sparse representation of a signal implicitly given as the solution of an operator equation or of an inverse problem requires more sophistication. We refer, for instance, to deconvolution and superresolution problems, image recovery and enhancing, and problems arising in geophysics and brain imaging. In these cases, thresholding has been combined with Landweber iterations to compute the solutions. In this talk we present a unified theory of iterative thresholding algorithms which includes soft, hard, and the so-called firm thresholding operators. In particular, we develop a variational approach of such algorithms which allows for a complete analysis of their convergence properties. As a matter of fact, despite their simplicity which makes them very appealing to users and their enormous impact for applications, iterative thresholding algorithms converges very slowly and might be impracticable in certain situations. By analyzing their typical convergence dynamics we propose acceleration methods based 1. on projected gradient iterations, 2. on alternating subspace corrections (domain decompositions.) Also for both these latter families of algorithms, a variational approach is fundamental in order to correctly analyse the convergence.

Holger Rauhut, University of Vienna

Sparse Recovery
Abstract. I will give an overview on the topic of sparse recovery with some emphasis on my own contributions. This emerging field, which is also refered to as compressed sensing or compressive sampling, was initiated in 2004 with pioneering work by Emmanuel Candès, Justin Romberg and Terence Tao, and independently by David Donoho.

A signal (vector, function) is called sparse if it has an expansion with only a small number of non-vanishing coefficients in terms of a suitable basis. Many real-world signals can be well-approximated by sparse ones. The basic idea of compressed sensing is that a sparse signal can be efficiently recovered from a number of linear non-adaptive measurements (inner products), which is much smaller than the ambient dimension of the signal (but of course larger than the sparsity, i.e., the number of non-vanishing coefficients). This surprising principle has many potential applications in signal and image processing. As reconstruction procedures, mainly l_1-minimization (basis pursuit) and greedy algorithms such as orthogonal matching pursuit have been investigated so far. All known good constructions of suitable linear measurements are of probabilistic nature.

As an important special case, it is possible to reconstruct a sparse trigonometric polynomial from random samples provided the number N of samples scales as N = O(M log(D)), where M is the number of non-vanishing Fourier coefficients and D the dimension of the corresponding space of trigonometric polynomials.

Extensions to multichannel (vector-valued) signals (distributed compressed sensing) and applications to the operator identification problem will be discussed briefly.

Vladimir Temlyakov, University of South Carolina

On the Lebesgue Type Inequalities for Greedy Approximation (Joint work with D.L. Donoho and M. Elad)
Abstract. We study the efficiency of greedy algorithms with regard to redundant dictionaries in Hilbert spaces. We obtain upper estimates for the errors of the Pure Greedy Algorithm and the Orthogonal Greedy Algorithm in terms of the best m-term approximations. We call such estimates the Lebesgue type inequalities. We prove the Lebesgue type inequalities for dictionaries with special structure. We assume that the dictionary has a property of mutual incoherence (the coherence parameter of the dictionary is small). We develop a new technique that, in particular, allowed us to get rid of an extra factor m^{1/2} in the Lebesgue type inequality for the Orthogonal Greedy Algorithm.

Fall 2006

Date	Time and Place	Speaker and Institution	Title and Abstract
Nov 20	2:15pm, WWH 513	Albert Cohen, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie Note special day, time and place	Nonlinear Approximation by Greedy Algorithms: Theory, Applications and Open Problems
Nov 20	3:30pm WWH 1302	Wolfgang Dahmen, Institut für Geometrie und Praktische Mathematik, RWTH Aachen Note special day, time and place	Universal Algorithms for Machine Learning
Dec 12	2:00pm, WWH 613	David Hammond, CIMS	Image Denoising with an Orientation-Adaptive Gaussian Scale Mixture Model

Fall 2005/Spring 2006

Date	Speaker and Institution	Title and Abstract
Sept 28	Radu Balan, Siemens Corporate Research	Noncommutative Wiener Lemma and Tracial State on the Banach Algebra of Time-Frequency Shift Operators
Jan 18	Laurent Demanet, California Institute of Technology	Curvelets, Wave Atoms and their numerical implementation
Feb 8	Gabriel Peyré, Ecole Polytechnique	Multiscale Geometry for Images and Textures
Feb 15	Özgür Yılmaz, University of British Columbia	The role of sparsity in blind source separation

Fall 2004

Date	Speaker and Institution	Title and Abstract
Aug 26	Onur Güleryüz, Polytechnic University and DoCoMo USA Labs, Inc.	Signal Processing with Sparse Statistical Models and Nonlinear Approximation
Sept 15	S. Muthu Muthukrishnan, Rutgers University	Nonuniform Sparse Approximation via Haar Wavelets
Sept 29	Ivan Selesnick, Polytechnic University	Motion-based 3-D wavelet frames and probability models for video processing
Oct 13	Thomas Yu, Rensselaer Polytechnic Institute	Multiscale Refinement Subdivision in Nonlinear and Geometric Settings
Oct 20	Cynthia Rudin, NYU Center for Neural Science	The Dynamics of Boosting
Dec 1	David Hammond, CIMS	Image representation via local multiscale orientation
Dec 8	M. Alex O. Vasilescu, Media Research Lab, CIMS	A Tensor Framework for Image Analysis (Vision) and Synthesis (Graphics)

Spring/Summer 2004

Date	Speaker and Institution	Title and Abstract
Feb 4	Ingrid Daubechies, Princeton University and CIMS	Recovering sparse expansions after noisy blur
Feb 11	Chai Wah Wu, IBM T. J. Watson Research Center	Error diffusion: recent developments in theory and applications
Feb 25	John J. Benedetto, University of Maryland	Fourier and wavelet frame constructions and applications
Mar 10	Eero Simoncelli, NYU Center for Neural Science and CIMS	Statistical models of photographic images with application to Bayes denoising
Mar 17	Ron DeVore, University of South Carolina	Estimators for Supervised Learning
Mar 24	Martin Strauss, AT&T Labs and University of Michigan	Improved time bounds for near-optimal sparse Fourier representations
Mar 31	Zhou Wang, Laboratory for Computational Vision, NYU	Perceptual image quality assessment: from error visibility to structural similarity
Apr 7	Ann Lee, Yale University	The Intrinsic Geometry of Natural Image Data and Learning by Diffusion
Apr 14	Frederik J. Simons, Princeton University	Time-frequency and time-scale analysis in geophysics: Multiwindow and multiwavelet methods in 1D, 2D and on the sphere
Apr 28	Gilad Lerman, CIMS	Multiscale Curve and Strip Constructions and Their Application to Microarray and ChIP-chip Data
May 5	Radu Balan, Siemens Corporate Research	Density and Redundancy of Irregular Gabor-like frames
June 9	Stephane Lafon, Yale University	Diffusion maps and geometric harmonics