Organizing Committee
Abstract

Harmonic analysis provides the mathematical backbone for modern signal and image processing. It also constitutes an important part of the foundation several scientific and engineering areas, including communication theory, control science, fluid dynamics, and electromagnetics, that underpin a much broader set of current applications. Although computer implementation of concepts from harmonic analysis is prevalent, relatively little attention is given to computational and numerical aspects of the discipline in its own literature. Further, many of the most capable young mathematicians working in this area have only modest exposure to the roles of such crucial computational considerations as finite data effects; e.g., How much error is introduced by truncating this infinite-series representation of a function in terms of a frame, and where will it be manifested?

On the other hand, new tools and ideas have entered the mainstream of harmonic analysis in recent years that have not yet become established in areas of applied mathematics where numerical and computational issues are routinely treated as integral aspects of problem formulation and methodological development. Among these are tools for non-orthogonal and overcomplete representations in linear spaces and the exploitation of sparsity and related (e.g., low rank) assumptions in inverse problems of various types. This research cluster seeks to bridge this perceived gap by (i) fostering understanding and appreciation of the computational perspective among harmonic analysts and (ii) increasing awareness of emerging mathematical tools and techniques in applied harmonic analysis among computational mathematicians.

Confirmed Speakers & Participants

Workshop Schedule

Monday, November 3, 2014
TimeEventLocationMaterials
8:30 - 8:55Registration - Research Cluster: Computational Challenges in Sparse and Redundant Representations11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45Tutorial: Redundant function representations based on Fourier series in theory and in practice - Daan Huybrechs, KU Leuven  
10:00 - 10:455 minute introductions11th Floor Lecture Hall 
11:00 - 11:45Discussion Session: Computational challenges of overcomplete representations11th Floor Lecture Hall 
12:00 - 2:30Break for Lunch  
2:30 - 3:15Discussion Session: Computational challenges of overcomplete representations11th Floor Lecture Hall 
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00Research Groups11th Floor Lecture Hall 
5:00 - 6:00Welcome Reception  
Tuesday, November 4, 2014
TimeEventLocationMaterials
9:00 - 9:45Research Talk: Fourier Continuation and the stability and accuracy of FC(Gram) algorithms - Mark Lyon, University of New Hampshire11th Floor Lecture Hall 
10:00 - 10:45Research Talk: Erasure robustness of frames and random frames - Yang Wang, Michigan State University11th Floor Lecture Hall 
11:00 - 11:45Research Talk: Smooth affine shear tight frames: wavelets, shearlets, and their connections - Xiaosheng Zhuang, City University of Hong Kong11th Floor Lecture Hall 
12:00 - 2:30Break for Lunch  
2:30 - 3:15Discussion Session: Frame-based approximation algorithms11th Floor Lecture Hall 
2:30 - 4:00Postdoc and Graduate Student Seminar11th Floor Conference Room 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
4:00 - 5:00Research Groups11th Floor Lecture Hall 
Wednesday, November 5, 2014
TimeEventLocationMaterials
9:00 - 9:45Tutorial: On phaseless reconstruction - Radu Balan, University of Maryland11th Floor Lecture Hall 
10:00 - 10:45Research Talk: Robust sparse phase retrieval made easy - Aditya Viswanathan, Michigan State University11th Floor Lecture Hall 
11:00 - 11:45Research Talks11th Floor Lecture Hall 
12:00 - 5:00Break for lunch and free time  
2:00 - 2:45Sharp L^p estimates for second order Riesz transforms on discrete abelian groups. - Stefanie Petermichl, Université de Toulouse III (Paul Sabatier)11th Floor Lecture Hall 
3:00 - 3:45The Dirichlet boundary problem for second order parabolic operators satisfying small Carleson condition - Martin Dindos, University of Edinburgh11th Floor Lecture Hall 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
Thursday, November 6, 2014
TimeEventLocationMaterials
9:00 - 9:45Research Talk: Computational issues of dual frame constructions - Ole Christensen, Technical University of Denmark11th Floor Lecture Hall 
9:00 - 10:00Professional development: Papers and journals10th Floor Classroom 
10:00 - 10:45Research Talk: Quantitative estimates for the finite section method - Karlheinz Gröchenig, Universität Wien11th Floor Lecture Hall 
11:00 - 11:45Discussion Session11th Lecture Hall 
12:00 - 2:30Break for Lunch  
2:30 - 3:15Discussion Session: Fast algorithms for Fourier Extensions from equispaced data - Roel Matthysen, KU Leuven11th Floor Lecture Hall 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
4:00 - 5:00Research Groups11th Floor Lecture Hall 
Friday, November 7, 2014
TimeEventLocationMaterials
9:00 - 9:45Research Talk: Quantization of frame expansions and compressed sensing measurements - Ozgur Yilmaz, University of British Columbia11th Floor Lecture Hall 
10:00 - 10:45Research Talks11th Floor Lecture Hall 
11:00 - 11:45Discussion Session: Recap, open problems and challenges11th Floor Lecture Hall 
12:00 - 2:30Break for Lunch  
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
Monday, November 10, 2014
TimeEventLocationMaterials
9:00 - 9:45Tutorial: Dynamical sampling - part I - Akram Aldroubi, Vanderbilt University 11th Floor Lecture Hall 
10:00 - 10:45Tutorial: Dynamical sampling - part II - Ilya Krishtal, Northern Illinois University11th Floor Lecture Hall 
11:00 - 11:455 minute introductions11th Floor Lecture Hall 
2:30 - 3:15Discussion Session: Algorithms for reconstruction in evolutionary systems11th Floor Lecture Hall 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
4:00 - 5:00Research Groups11th Floor Lecture Hall 
Tuesday, November 11, 2014
TimeEventLocationMaterials
2:30 - 4:00Postdoc and Graduate Student Seminar11th Floor Conference Room 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
Wednesday, November 12, 2014
TimeEventLocationMaterials
9:00 - 9:45Tutorial: Sampling of multivariate fields and related problems - Karlheinz Gröchenig, Universität Wien11th Floor Lecture Hall 
10:00 - 10:45Research Talk: Generalized sampling and stable recovery of multivariate signals from nonuniform Fourier measurements - Milana Gataric, University of Cambridge11th Floor Lecture Hall 
11:00 - 11:45Discussion Session11th Floor Lecture Hall 
2:30 - 3:15Discussion Session: Nonstandard sampling11th Floor Lecture Hall 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
4:00 - 5:00Research Groups11th Floor Lecture Hall 
Thursday, November 13, 2014
TimeEventLocationMaterials
9:00 - 9:45Research Talks: Reproducing Formulas for Generalized Translation Invariant Systems - Jakob Lemvig, Technical University of Denmark11th Floor Lecture Hall 
10:00 - 10:45Research Talk: Mobile sampling of bandlimited fields. Reconstruction of bandlimited functions from samples taken along continuous trajectories - Jose-Luis Romero, University of Vienna11th Floor Lecture Hall 
10:00 - 10:45Research Talk: Mobile sampling of bandlimited fields. Reconstruction of bandlimited functions from samples taken along continuous trajectories - Jose-Luis Romero, University of Vienna11th Floor Lecture Hall 
11:00 - 11:45Discussion Session11th Floor Lecture Hall 
2:30 - 3:15Discussion Session: Mobile sampling11th Floor Lecture Hall 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
4:00 - 5:00Research Groups11th Floor Lecture Hall 
Friday, November 14, 2014
TimeEventLocationMaterials
10:00 - 10:45Dynamic Sampling III - Jacqueline Davis, Vanderbilt University11th Floor Lecture Hall 
11:00 - 11:45Discussion Session: Recap, open problems and challenges11th Floor Lecture Hall 
12:30 - 1:30Professional development: Grant proposals11th Floor Conference Room 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
Monday, November 17, 2014
TimeEventLocationMaterials
9:00 - 9:45Tutorial: Direct Methods for Reconstruction of Functions and their Edges from Non-Uniform Fourier Data - Aditya Viswanathan, Michigan State University11th Floor Lecture Hall 
10:00 - 10:455 minute introductions11th Floor Lecture Hall 
11:00 - 11:45Research Talk: Neutron tomography: Improving imaging techniques that enable design of fast scanning techniques that sample sparsely in reciprocal space while maintaining image fidelity. - Rick Archibald, Oak Ridge National Laboratory11th Floor Lecture Hall 
12:00 - 2:30Break for Lunch  
2:30 - 3:30Representation and coding of signal distances- Comparing signals in the cloud - Petros Boufounos, Mitsubishi Electric Research Laboratories11th Floor Lecture Hall 
2:30 - 3:15Discussion Session: Applications to radar, MRI, tomography, etc10th Floor Classroom 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
4:00 - 5:00Research Groups11th Floor Lecture Hall 
4:30 - 5:30Approximation Seminar - TBA10th Floor Classroom 
Tuesday, November 18, 2014
TimeEventLocationMaterials
9:00 - 9:45Research Talk: Infinite-dimensional l1 minimization and function approximation - Ben Adcock, Simon Fraser University11th Floor Lecture Hall 
10:00 - 10:45Research Talk: Recovering spectral accuracy for functions with end-point singularities - Chi-Wang Shu, Brown University11th Floor Lecture Hall 
11:00 - 11:45Research Talk: Edge detection from Fourier data in 1-D and 2-D - Guohui Song, Clarkson University11th Floor Lecture Hall 
12:00 - 2:30Break for Lunch  
2:30 - 4:00Postdoc and Graduate Student Seminar11th Floor Conference Room 
2:30 - 3:15Discussion Session11th Floor Lecture Hall 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
4:00 - 5:00Research Groups11th FLoor Lecture Hall 
Wednesday, November 19, 2014
TimeEventLocationMaterials
9:00 - 9:45Research Talk: Reconstruction of 3D objects from their 2D cross-sections by a subdivision scheme for sets - Nira Dyn, Tel Aviv University11th Floor Lecture Hall 
10:00 - 10:45Research Talk: Super-resolution and prolate functions: Why the two appear in the same sentence - Armin Eftekhari, Colorado School of Mines11th Floor Lecture Hall 
11:00 - 11:45Discussion Session11th Floor Lecture Hall 
12:00 - 5:00Break for lunch and free time  
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
Thursday, November 20, 2014
TimeEventLocationMaterials
10:00 - 10:45Research Talk: Multireference alignment problems - Afonso Bandeira, Princeton University11th Floor Lecture Hall 
11:00 - 11:45Nearest neighbor based greedy coordinate descent - Pradeep Ravikumar\, University of Texas\, Austin11th Floor Lecture Hall 
11:00 - 11:45Nearest neighbor based greedy coordinate descent - Pradeep Ravikumar, University of Texas, Austin11th Floor Lecture Hall 
12:00 - 2:30Break for Lunch  
2:30 - 3:15Discussion Session11th Floor Lecture Hall 
3:30 - 4:00Coffee Break11th Floor Collaborative Space 
4:00 - 5:00Research Groups11th Floor Lecture Hall 
Friday, November 21, 2014
TimeEventLocationMaterials
10:00 - 10:45Research Groups11th Floor Lecture Hall 
11:00 - 11:45Discussion Session: Recap, open problems and challenges11th Floor Lecture Hall 
12:00 - 2:30Break for Lunch  
3:30 - 4:00Coffee Break11th Floor Collaborative Space 

Associated Semester Workshops

High-dimensional Approximation
Approximation, Integration, and Optimization
Discrepancy Theory