Exploiting structure in wavelet-based bayesian compressive sensing

Lihan He, Lawrence Carin

Research output: Contribution to journalArticlepeer-review

373 Scopus citations

Abstract

Bayesian compressive sensing (CS) is considered for signals and images that are sparse in a wavelet basis. The statistical structure of the wavelet coefficients is exploited explicitly in the proposed model, and, therefore, this framework goes beyond simply assuming that the data are compressible in a wavelet basis. The structure exploited within the wavelet coefficients is consistent with that used in wavelet-based compression algorithms. A hierarchical Bayesian model is constituted, with efficient inference via Markov chain Monte Carlo (MCMC) sampling. The algorithm is fully developed and demonstrated using several natural images, with performance comparisons to many state-of-the-art compressive-sensing inversion algorithms. © 2009 IEEE.
Original languageEnglish (US)
Pages (from-to)3488-3497
Number of pages10
JournalIEEE Transactions on Signal Processing
Volume57
Issue number9
DOIs
StatePublished - Sep 3 2009
Externally publishedYes

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