SenSIP Distinguished Lecturer Seminar Series
Computable Performance Analysis of Sparse Recovery
Arye Nehorai, IEEE Fellow
Tuesday, January 20, 2015
Goldwater Center (GWC) 487, Tempe campus [map]
The last decade has witnessed burgeoning developments in the reconstruction of signals based on exploiting their low-dimensional structures, particularly their sparsity, block-sparsity, and low-rankness. The reconstruction performance of these signals is heavily dependent on the structure of the operating matrix used in sensing. The quality of these matrices in the context of signal recovery is usually quantified by the restricted isometry constant and its variants. However, the restricted isometry constant and its variants are extremely difficult to compute. We present a framework for analytically computing the performance of the recovery of signals with sparsity structures. We define a family of incoherence measures to quantify the goodness of arbitrary sensing matrices. Our primary contribution is the design of efficient algorithms, based on linear programming and second order cone programming, to compute these incoherence measures. As a by-product, we implement efficient algorithms to verify sufficient conditions for exact signal recovery in the noise-free case. The utility of the proposed incoherence measures lies in their relationship to the performance of reconstruction methods. We derive closed-form expressions of bounds on the recovery errors of convex relaxation algorithms in terms of these measures.
Arye Nehorai is the Eugene and Martha Lohman Professor and Chair of the Preston M. Green Department of Electrical and Systems Engineering, professor in the Department of Biomedical Engineering and in the Division of Biology and Biomedical Studies at Washington University in St. Louis (WUSTL). Under his leadership as department chair, the undergraduate enrollment has more than tripled in the last four years. He received the B.Sc. and M.Sc. degrees from the Technion, Israel and the Ph.D. from Stanford University, California. Nehorai had served as Editor-in-Chief of the IEEE Transactions on Signal Processing from 2000 to 2002. From 2003 to 2005 he was the vice president (Publications) of the IEEE Signal Processing Society (SPS), the Chair of the Publications Board, and a member of the Executive Committee of this Society. Nehorai received the 2006 IEEE SPS Technical Achievement Award and the 2010 IEEE SPS Meritorious Service Award. He was elected Distinguished Lecturer of the IEEE SPS for a term lasting from 2004 to 2005. He received several best paper awards in IEEE journals and conferences. He is a Fellow of the IEEE, the Royal Statistical Society, and the AAAS.
Sponsored by the SenSIP Center and NSF I/UCRC : sensip.asu.edu
Technical Co-Sponsorship by the IEEE Signal Processing and Communications Chapter, Phoenix Section