Compressive Imaging using Approximate Message Passing and a Markov-Tree Prior

TL;DR

This paper introduces a new compressive imaging algorithm that combines approximate message passing with a Markov-tree prior, leveraging wavelet sparsity and persistence for improved image reconstruction.

Contribution

It presents a novel turbo belief propagation method that integrates AMP and HMT modeling, achieving state-of-the-art performance with reduced complexity.

Findings

Outperforms existing schemes in image reconstruction quality

Reduces computational complexity significantly

Effective exploitation of wavelet structure in compressive imaging

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.