Abstract-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.
For example, Som and Schniter REF modeled the structure of the wavelet coefficients by a hidden Markov tree (HMT), and applied a turbo scheme that alternates between inference on the HMT structure with standard belief propagation and inference on the compressed sensing measurement structure with the generalized approximate message passing algorithm.
Compressive Imaging using Approximate Message Passing and a Markov-Tree Prior
ArXiv
ArXiv
Computer Science