## Applied and Computational Harmonic Analysis: 2011-2014

### Overview

Applied and Computational Harmonic Analysis is an interdisciplinary branch of modern mathematics and is concerned with the applied and computational aspects of harmonic analysis and approximation theory, with special emphasis on wavelet analysis, time-frequency analysis, redundant representations, and their applications in many areas such as signal / image processing, computer graphics, and numerical algorithms in scientific computing. Many problems in sciences and applications are multiscale in nature. One of the core goals of applied and computational harmonic analysis is to develop and study various mathematical multiscale based methods that can represent and approximate a given set of functions / signals / data efficiently and sparsely with fast algorithms. For example, signals with multiscale structure have sparse representations with respect to wavelet bases and this makes wavelet analysis a desired tool in many areas of sciences and applications. The impact of applied and computational harmonic analysis has been evidenced by many successes: wavelet based methods for image compression standard JPEG 2000 and for signal / image denoising, subdivision scheme based methods in computer graphics and visualization / simulation in medical imaging and movie / game industry, new efficient Sigma-delta schemes in analog-to-digital conversion in signal processing, adaptive wavelet methods in scientific computing for the numerical solution to partial differential equations (PDEs).

### CRG Leaders

Bin Han (University of Alberta)

Rong-Qing Jia (University of Alberta)

Elena Braverman (University of Calgary)

Ozgur Yilmaz (University of British Columbia)

### Participating Faculty from PIMS Universities

University of Alberta: Bin Han, Rong-Qing Jia, Xiaobo Li, Peter Minev, Yau Shu Wong

University of British Columbia: Felix J. Herrmann, Bernard Shizgal, Ozgur Yilmaz

University of Calgary: Len Bos, Elena Braverman

University of Victoria: Michael Adams

University of Washington: Thomas Duchamp

### Scientific Activities

International Conference on Applied Harmonic Analysis and Multiscale Computing, July 25-28, 2011, University of Alberta

Computational Harmonic Analysis Summer School, July 29-31, 2011, University of Alberta

**Joint Alberta-British Columbia 4-day Seminars**

Alberta-British Columbia Seminar in Harmonic Analysis, August 7-10, 2012, UBC.

Applied Harmonic Analysis Conference, August 26-30, 2013, Calgary.

PIMS-BIRS Workshop: Recent Progress on Applied and Computational Harmonic Analysis, August 30 ‐ September 1, 2013, Banff, Organisers: Elena Braverman (UCalgary), Bin Han (University of Alberta), Ozgur Yilmaz (University of British Columbia)

### Reports

### Research Impacts

Wavelet Analysis and its Applications

Convergence of theta-method for time-variable equations

Efficient quantization methods for compressed sensing

### Visitors:

Raymond H. Chan (Chinese University of Hong Kong, Hong Kong)

Charles A. Micchelli (State University of New York at Albany, USA)

Yuesheng Xu (Syracuse University, USA)

Qun Mo (Zhejiang University, China)

Martin Ehler (University of Maryland, USA)

### Postdoctoral Fellows

Kun Wang, Supervisors: Rong-Qing Jia (University of Alberta), Yau Shu Wong (University of Alberta), September 2011-August 2013

Enrico Au-Yeung, Supervisor: Ozgur Yilmaz (UBC), September 2011-August 2012