Exploiting Structure in Wavelet-Based Bayesian Compressive Sensing

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...

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Bibliographic Details
Published inIEEE transactions on signal processing Vol. 57; no. 9; pp. 3488 - 3497
Main Authors Lihan He, Carin, L.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.09.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Applied sciences
Bayesian analysis
Bayesian methods
Bayesian signal processing
compression
Compression algorithms
Computer simulation
Detection
Discrete wavelet transforms
Exact sciences and technology
Hyperspectral imaging
Image coding
Image processing
Inference algorithms
Information, signal and communications theory
Magnetic field measurement
Mathematical models
Miscellaneous
Monte Carlo methods
Sampling, quantization
Signal and communications theory
Signal processing
Signal processing algorithms
Signal representation. Spectral analysis
Signal, noise
sparseness
Telecommunications and information theory
Transform coding
Wavelet
Wavelet coefficients
wavelets
Performance evaluation
State of the art
Image processing
Inverse problem
Wavelets
sparseness
Image analysis
MCMC algorithm
Wavelet transformation
Wavelet base
Signal processing
Bayes methods
Hierarchical system
Sampling
Bayesian signal processing
compression
Signal analysis
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2009.2022003