Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 60, Issue 7, Pages 3439-3448Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2012.2191780
Keywords
Belief propagation; compressed sensing; hidden Markov tree; image reconstruction; structured sparsity
Categories
Funding
- NSF [CCF-1018368]
- AFOSR [FA9550-06-1-0324]
- DARPA/ONR [N66001-10-1-4090]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1018368] Funding Source: National Science Foundation
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We propose a novel algorithm for compressive imaging that exploits both the sparsity and persistence across scales found in the 2D wavelet transform coefficients of natural images. Like other recent works, we model wavelet structure using a hidden Markov tree (HMT) but, unlike other works, ours is based on loopy belief propagation (LBP). For LBP, we adopt a recently proposed turbo message passing schedule that alternates between exploitation of HMT structure and exploitation of compressive-measurement structure. For the latter, we leverage Donoho, Maleki, and Montanari's recently proposed approximate message passing (AMP) algorithm. Experiments with a large image database suggest that, relative to existing schemes, our turbo LBP approach yields state-of-the-art reconstruction performance with substantial reduction in complexity.
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