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Fall 2014 Research Clusters

To participate in a research cluster please apply through the semester program visitors application. Indicate which research cluster you are applying to in the "other comments" section of the application.


Research Cluster: Computational Challenges in Sparse and Redundant Representations (November 3-21, 2014)


Organizers:
Description

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.


  • Ben Adcock
    (Simon Fraser University)
  • Akram Aldroubi
    (Vanderbilt University)
  • Rick Archibald
    (Oak Ridge National Laboratory)
  • Amir Averbuch
    (Tel Aviv University)
  • Radu Balan
    (University of Maryland)
  • Afonso Bandeira
    (Princeton University)
  • Ole Christensen
    (Technical University of Denmark)
  • Jacqueline Davis
    (Vanderbilt University)
  • Nira Dyn
    (Tel Aviv University)
  • Milana Gataric
    (University of Cambridge)
  • Anne Gelb
    (Arizona State University)
  • Karlheinz Gröchenig
    (Universität Wien)
  • Philipp Grohs
    (ETH)
  • Daan Huybrechs
    (KU Leuven)
  • Ilya Krishtal
    (Northern Illinois University)
  • Jakob Lemvig
    (Technical University of Denmark)
  • Mark Lyon
    (University of New Hampshire)
  • Roel Matthysen
    (KU Leuven)
  • Dustin Mixon
    (Air Force Institute of Technology)
  • Rodrigo Platte
    (Arizona State University)
  • Jose Luis Romero
    (Universität Wien)
  • Chi-Wang Shu
    (Brown University)
  • Guohui Song
    (Clarkson University)
  • Aditya Viswanathan
    (Michigan State University)
  • Yang Wang
    (Michigan State University)
  • Xiaosheng Zhuang
    (City University of Hong Kong)
MondayNovember 3, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
8:30 - 8:55Registration - Research Cluster: Computational Challenges in Sparse and Redundant Representations11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:45Tutorial: Redundant function representations based on Fourier series in theory and in practiceDaan 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

TuesdayNovember 4, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Research Talk: Fourier Continuation and the stability and accuracy of FC(Gram) algorithmsMark Lyon, University of New Hampshire11th Floor Lecture Hall
10:00 - 10:45Research Talk: Erasure robustness of frames and random framesYang Wang, Michigan State University11th Floor Lecture Hall
11:00 - 11:45Research Talk: Smooth affine shear tight frames: wavelets, shearlets, and their connectionsXiaosheng 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
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 5:00Research Groups11th Floor Lecture Hall

WednesdayNovember 5, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Tutorial: On phaseless reconstructionRadu Balan, University of Maryland11th Floor Lecture Hall
10:00 - 10:45Research Talk: Robust sparse phase retrieval made easyAditya Viswanathan, Michigan State University11th Floor Lecture Hall
11:00 - 11:45Research Talks11th Floor Lecture Hall
12:00 - 5:00Break for lunch and free time

ThursdayNovember 6, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Research Talks11th Floor Lecture Hall
10:00 - 10:45Research Talks11th Floor Lecture Hall
11:00 - 11:45Research Talks11th Lecture Hall
12:00 - 2:30Break for Lunch
2:30 - 3:15Discussion Session: Sampling and reconstruction with frames11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 5:00Research Groups11th Floor Lecture Hall

FridayNovember 7, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Research Talk: Computational issues of dual frame constructionsOle Christensen, Technical University of Denmark11th Floor Lecture Hall
10:00 - 10:45Research Talk: Quantitative estimates for the finite section methodKarlheinz Grochenig, University of Vienna11th Floor Lecture Hall
11:00 - 11:45Discussion Session: Recap, open problems and challenges11th Floor Lecture Hall
12:00 - 2:30Break for Lunch

MondayNovember 10, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Tutorial: Dynamical samplingAkram Aldroubi, Vanderbilt University 11th Floor Lecture Hall
10:00 - 10:455 minute introductions11th Floor Lecture Hall
11:00 - 11:455 minute introductions11th Floor Lecture Hall
12:00 - 2:30Break for Lunch
2:30 - 3:15Discussion Session: Algorithms for reconstruction in evolutionary systems11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 5:00Research Groups11th Floor Lecture Hall

TuesdayNovember 11, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 5:00No Scheduled Research Cluster Events in Observance of Veteran's DayICERM is open

WednesdayNovember 12, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Tutorial: Sampling of multivariate fields and related problemsKarlheinz Gröchenig, Universität Wien11th Floor Lecture Hall
10:00 - 10:45Research Talk11th Floor Lecture Hall
11:00 - 11:45Research Talks11th Floor Lecture Hall
12:00 - 2:30Break for Lunch
2:30 - 3:15Discussion Session: Mobile and nonstandard sampling11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 5:00Research Groups11th Floor Lecture Hall

ThursdayNovember 13, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Research Talk: Mobile sampling of bandlimited fields. Reconstruction of bandlimited functions from samples taken along continuous trajectoriesJose-Luis Romero, University of Vienna11th Floor Lecture Hall
10:00 - 10:45Research Talks11th Floor Lecture Hall
11:00 - 11:45Research Talks11th Floor Lecture Hall
12:00 - 2:30Break for Lunch
2:30 - 3:15Discussion Session: Mobile and nonstandard sampling11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 5:00Research Groups11th Floor Lecture Hall

FridayNovember 14, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Research Talks11th 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

MondayNovember 17, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Tutorial: Direct Methods for Reconstruction of Functions and their Edges from Non-Uniform Fourier DataAditya Viswanathan, Michigan State University11th Floor Lecture Hall
10:00 - 10:455 minute introductions11th Floor Lecture Hall
11:00 - 11:455 minute introductions11th Floor Lecture Hall
12:00 - 2:30Break for Lunch
2:30 - 3:15Discussion Session: Convergence 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 - 6:00Light Reception11th Floor Collaborative Space

TuesdayNovember 18, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Research Talks11th Floor Lecture Hall
10:00 - 10:45Research Talks11th Floor Lecture Hall
11:00 - 11:45Research Talks11th Floor Lecture Hall
12:00 - 2:30Break for Lunch
2:30 - 3:15Discussion Session: Applications to radar, MRI, tomography, etc11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 5:00Research Groups11th FLoor Lecture Hall

WednesdayNovember 19, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Tutorial11th Floor Lecture Hall
10:00 - 10:45Research Talks11th Floor Lecture Hall
11:00 - 11:45Research Talks11th Floor Lecture Hall
12:00 - 5:00Break for lunch and free time

ThursdayNovember 20, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Research Talks11th Floor Lecture Hall
10:00 - 10:45Research Talks11th Floor Lecture Hall
11:00 - 11:45Research Talks11th Floor Lecture Hall
12:00 - 2:30Break for Lunch
2:30 - 3:15Discussion Session: Applications to radar, MRI, tomography, etc11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 5:00Research Groups11th Floor Lecture Hall

FridayNovember 21, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Research Talks11th 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