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.
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