A Sparsity Basis Selection Method for Compressed Sensing

Abstract

This letter presents a new sparsity basis selection compressed sensing method (SBSCS) for improving signal reconstruction from compressed sensing (CS) measurements. Based on the observation that different classes of transform cause different sparsity expressions and better sparsity expression leads to better signal recovery, the proposed SBSCS method searches the best class of transform and basis in a set of redundant tree-structured dictionaries by nesting sparsity maximization within the CS minimization. The SBSCS method adaptively selects the class of transform and basis with the best sparsity measure at each ℓ1 iteration and converges quickly to the final class of transform and basis. Numerical experiments show that the proposed SBSCS method improves the quality of signal recovery over the existing best basis compressed sensing method (BBCS) proposed by Peyré in 2010.

Department(s)

Electrical and Computer Engineering

Keywords and Phrases

Iterative methods; Numerical methods; Signal reconstruction; Basis selection; Compressive sensing; Different class; Numerical experiments; Redundant trees; Signal recovery; Sparsity; Sparsity measures; Compressed sensing; Compressed sensing (CS); Sparsity maximization

International Standard Serial Number (ISSN)

1070-9908

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2015 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Oct 2015

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