CUED Publications database

Convex approaches to model wavelet sparsity patterns

Rao, NS and Nowak, RD and Wright, SJ and Kingsbury, NG (2011) Convex approaches to model wavelet sparsity patterns. Proceedings - International Conference on Image Processing, ICIP. pp. 1917-1920. ISSN 1522-4880

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Abstract

Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees (HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix produces a linear mixing of the simple Markovian dependency structure. This leads to reconstruction problems that are non-convex optimizations. Past work has dealt with this issue by resorting to greedy or suboptimal iterative reconstruction methods. In this paper, we propose new modeling approaches based on group-sparsity penalties that leads to convex optimizations that can be solved exactly and efficiently. We show that the methods we develop perform significantly better in de-convolution and compressed sensing applications, while being as computationally efficient as standard coefficient-wise approaches such as lasso. © 2011 IEEE.

Item Type: Article
Uncontrolled Keywords: compressed sensing deconvolution wavelet modeling
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:23
Last Modified: 29 Nov 2014 19:03
DOI: 10.1109/ICIP.2011.6115845