SILO



The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group

3M

with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

Convex approaches to model wavelet coefficients

Nikhil Rao, Student of Professor Nowak

Date and Time: Feb 16, 2011 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building

Abstract:

Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees. However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix leads to reconstruction problems that are intractable or non-convex optimizations. Past work has dealt with this issue by resorting to greedy or suboptimal iterative reconstruction methods. We propose new modeling approaches based on group sparsity of the wavelet coefficients that leads to convex optimizations that can be solved efficiently. We show that the methods we develop perform significantly better in deconvolution and compressed sensing applications, while being as computationally efficient as standard coefficient-wise approaches such as Lasso. (Joint work with Prof. Robert Nowak and Prof. Stephen Wright )