##### Organizing Committee

- Ben Adcock
*Simon Fraser University* - Doug Cochran
*Arizona State University* - Anne Gelb
*Arizona State University* - Karlheinz Gröchenig
*Universit?_t Wien* - Yang Wang
*The Hong Kong University of Science and Technology*

##### 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

- Ben Adcock
- Akram Aldroubi
- Rick Archibald
- Radu Balan
- Afonso Bandeira
- Ole Christensen
- Jaqueline Davis
- Nira Dyn
- Milana Gataric
- Anne Gelb
- Karlheinz Gröchenig
- Daan Huybrechs
- Ilya Krishtal
- Jakob Lemvig
- Mark Lyon
- Roel Matthysen
- Dustin Mixon
- Rodrigo Platte
- Jose Luis Romero
- Chi-Wang Shu
- Guohui Song
- Aditya Viswanathan
- Yang Wang
- Xiaosheng Zhuang

#### Workshop Schedule

##### Monday, November 3, 2014

Time | Event | Location | Materials |
---|---|---|---|

8:30 - 8:55 | Registration - Research Cluster: Computational Challenges in Sparse and Redundant Representations | 11th Floor Collaborative Space | |

8:55 - 9:00 | Welcome - ICERM Director | 11th Floor Lecture Hall | |

9:00 - 9:45 | Tutorial: Redundant function representations based on Fourier series in theory and in practice - Daan Huybrechs, KU Leuven | ||

10:00 - 10:45 | 5 minute introductions | 11th Floor Lecture Hall | |

11:00 - 11:45 | Discussion Session: Computational challenges of overcomplete representations | 11th Floor Lecture Hall | |

12:00 - 2:30 | Break for Lunch | ||

2:30 - 3:15 | Discussion Session: Computational challenges of overcomplete representations | 11th Floor Lecture Hall | |

3:30 - 4:00 | Coffee/Tea Break | 11th Floor Collaborative Space | |

4:00 - 5:00 | Research Groups | 11th Floor Lecture Hall | |

5:00 - 6:00 | Welcome Reception |

##### Tuesday, November 4, 2014

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:45 | Research Talk: Fourier Continuation and the stability and accuracy of FC(Gram) algorithms - Mark Lyon, University of New Hampshire | 11th Floor Lecture Hall | |

10:00 - 10:45 | Research Talk: Erasure robustness of frames and random frames - Yang Wang, Michigan State University | 11th Floor Lecture Hall | |

11:00 - 11:45 | Research Talk: Smooth affine shear tight frames: wavelets, shearlets, and their connections - Xiaosheng Zhuang, City University of Hong Kong | 11th Floor Lecture Hall | |

12:00 - 2:30 | Break for Lunch | ||

2:30 - 3:15 | Discussion Session: Frame-based approximation algorithms | 11th Floor Lecture Hall | |

2:30 - 4:00 | Postdoc and Graduate Student Seminar | 11th Floor Conference Room | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space | |

4:00 - 5:00 | Research Groups | 11th Floor Lecture Hall |

##### Wednesday, November 5, 2014

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:45 | Tutorial: On phaseless reconstruction - Radu Balan, University of Maryland | 11th Floor Lecture Hall | |

10:00 - 10:45 | Research Talk: Robust sparse phase retrieval made easy - Aditya Viswanathan, Michigan State University | 11th Floor Lecture Hall | |

11:00 - 11:45 | Research Talks | 11th Floor Lecture Hall | |

12:00 - 5:00 | Break for lunch and free time | ||

2:00 - 2:45 | Sharp 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 - 3:45 | The Dirichlet boundary problem for second order parabolic operators satisfying small Carleson condition - Martin Dindos, University of Edinburgh | 11th Floor Lecture Hall | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space |

##### Thursday, November 6, 2014

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:45 | Research Talk: Computational issues of dual frame constructions - Ole Christensen, Technical University of Denmark | 11th Floor Lecture Hall | |

9:00 - 10:00 | Professional development: Papers and journals | 10th Floor Classroom | |

10:00 - 10:45 | Research Talk: Quantitative estimates for the finite section method - Karlheinz Gröchenig, Universität Wien | 11th Floor Lecture Hall | |

11:00 - 11:45 | Discussion Session | 11th Lecture Hall | |

12:00 - 2:30 | Break for Lunch | ||

2:30 - 3:15 | Discussion Session: Fast algorithms for Fourier Extensions from equispaced data - Roel Matthysen, KU Leuven | 11th Floor Lecture Hall | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space | |

4:00 - 5:00 | Research Groups | 11th Floor Lecture Hall |

##### Friday, November 7, 2014

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:45 | Research Talk: Quantization of frame expansions and compressed sensing measurements - Ozgur Yilmaz, University of British Columbia | 11th Floor Lecture Hall | |

10:00 - 10:45 | Research Talks | 11th Floor Lecture Hall | |

11:00 - 11:45 | Discussion Session: Recap, open problems and challenges | 11th Floor Lecture Hall | |

12:00 - 2:30 | Break for Lunch | ||

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space |

##### Monday, November 10, 2014

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:45 | Tutorial: Dynamical sampling - part I - Akram Aldroubi, Vanderbilt University | 11th Floor Lecture Hall | |

10:00 - 10:45 | Tutorial: Dynamical sampling - part II - Ilya Krishtal, Northern Illinois University | 11th Floor Lecture Hall | |

11:00 - 11:45 | 5 minute introductions | 11th Floor Lecture Hall | |

2:30 - 3:15 | Discussion Session: Algorithms for reconstruction in evolutionary systems | 11th Floor Lecture Hall | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space | |

4:00 - 5:00 | Research Groups | 11th Floor Lecture Hall |

##### Tuesday, November 11, 2014

Time | Event | Location | Materials |
---|---|---|---|

2:30 - 4:00 | Postdoc and Graduate Student Seminar | 11th Floor Conference Room | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space |

##### Wednesday, November 12, 2014

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:45 | Tutorial: Sampling of multivariate fields and related problems - Karlheinz Gröchenig, Universität Wien | 11th Floor Lecture Hall | |

10:00 - 10:45 | Research Talk: Generalized sampling and stable recovery of multivariate signals from nonuniform Fourier measurements - Milana Gataric, University of Cambridge | 11th Floor Lecture Hall | |

11:00 - 11:45 | Discussion Session | 11th Floor Lecture Hall | |

2:30 - 3:15 | Discussion Session: Nonstandard sampling | 11th Floor Lecture Hall | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space | |

4:00 - 5:00 | Research Groups | 11th Floor Lecture Hall |

##### Thursday, November 13, 2014

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:45 | Research Talks: Reproducing Formulas for Generalized Translation Invariant Systems - Jakob Lemvig, Technical University of Denmark | 11th Floor Lecture Hall | |

10:00 - 10:45 | Research Talk: Mobile sampling of bandlimited fields. Reconstruction of bandlimited functions from samples taken along continuous trajectories - Jose-Luis Romero, University of Vienna | 11th Floor Lecture Hall | |

10:00 - 10:45 | Research Talk: Mobile sampling of bandlimited fields. Reconstruction of bandlimited functions from samples taken along continuous trajectories - Jose-Luis Romero, University of Vienna | 11th Floor Lecture Hall | |

11:00 - 11:45 | Discussion Session | 11th Floor Lecture Hall | |

2:30 - 3:15 | Discussion Session: Mobile sampling | 11th Floor Lecture Hall | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space | |

4:00 - 5:00 | Research Groups | 11th Floor Lecture Hall |

##### Friday, November 14, 2014

Time | Event | Location | Materials |
---|---|---|---|

10:00 - 10:45 | Dynamic Sampling III - Jacqueline Davis, Vanderbilt University | 11th Floor Lecture Hall | |

11:00 - 11:45 | Discussion Session: Recap, open problems and challenges | 11th Floor Lecture Hall | |

12:30 - 1:30 | Professional development: Grant proposals | 11th Floor Conference Room | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space |

##### Monday, November 17, 2014

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:45 | Tutorial: Direct Methods for Reconstruction of Functions and their Edges from Non-Uniform Fourier Data - Aditya Viswanathan, Michigan State University | 11th Floor Lecture Hall | |

10:00 - 10:45 | 5 minute introductions | 11th Floor Lecture Hall | |

11:00 - 11:45 | Research 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 Laboratory | 11th Floor Lecture Hall | |

12:00 - 2:30 | Break for Lunch | ||

2:30 - 3:30 | Representation and coding of signal distances- Comparing signals in the cloud - Petros Boufounos, Mitsubishi Electric Research Laboratories | 11th Floor Lecture Hall | |

2:30 - 3:15 | Discussion Session: Applications to radar, MRI, tomography, etc | 10th Floor Classroom | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space | |

4:00 - 5:00 | Research Groups | 11th Floor Lecture Hall | |

4:30 - 5:30 | Approximation Seminar - TBA | 10th Floor Classroom |

##### Tuesday, November 18, 2014

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:45 | Research Talk: Infinite-dimensional l1 minimization and function approximation - Ben Adcock, Simon Fraser University | 11th Floor Lecture Hall | |

10:00 - 10:45 | Research Talk: Recovering spectral accuracy for functions with end-point singularities - Chi-Wang Shu, Brown University | 11th Floor Lecture Hall | |

11:00 - 11:45 | Research Talk: Edge detection from Fourier data in 1-D and 2-D - Guohui Song, Clarkson University | 11th Floor Lecture Hall | |

12:00 - 2:30 | Break for Lunch | ||

2:30 - 4:00 | Postdoc and Graduate Student Seminar | 11th Floor Conference Room | |

2:30 - 3:15 | Discussion Session | 11th Floor Lecture Hall | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space | |

4:00 - 5:00 | Research Groups | 11th FLoor Lecture Hall |

##### Wednesday, November 19, 2014

Time | Event | Location | Materials |
---|---|---|---|

9:00 - 9:45 | Research Talk: Reconstruction of 3D objects from their 2D cross-sections by a subdivision scheme for sets - Nira Dyn, Tel Aviv University | 11th Floor Lecture Hall | |

10:00 - 10:45 | Research Talk: Super-resolution and prolate functions: Why the two appear in the same sentence - Armin Eftekhari, Colorado School of Mines | 11th Floor Lecture Hall | |

11:00 - 11:45 | Discussion Session | 11th Floor Lecture Hall | |

12:00 - 5:00 | Break for lunch and free time | ||

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space |

##### Thursday, November 20, 2014

Time | Event | Location | Materials |
---|---|---|---|

10:00 - 10:45 | Research Talk: Multireference alignment problems - Afonso Bandeira, Princeton University | 11th Floor Lecture Hall | |

11:00 - 11:45 | Nearest neighbor based greedy coordinate descent - Pradeep Ravikumar\, University of Texas\, Austin | 11th Floor Lecture Hall | |

11:00 - 11:45 | Nearest neighbor based greedy coordinate descent - Pradeep Ravikumar, University of Texas, Austin | 11th Floor Lecture Hall | |

12:00 - 2:30 | Break for Lunch | ||

2:30 - 3:15 | Discussion Session | 11th Floor Lecture Hall | |

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space | |

4:00 - 5:00 | Research Groups | 11th Floor Lecture Hall |

##### Friday, November 21, 2014

Time | Event | Location | Materials |
---|---|---|---|

10:00 - 10:45 | Research Groups | 11th Floor Lecture Hall | |

11:00 - 11:45 | Discussion Session: Recap, open problems and challenges | 11th Floor Lecture Hall | |

12:00 - 2:30 | Break for Lunch | ||

3:30 - 4:00 | Coffee Break | 11th Floor Collaborative Space |