Back in December 2010, I was very interested with a new reconstruction called Turbo-AMP. Phil Schniter just let me know it is out. Thanks Phil. First here is the paper: Compressive Imaging using Approximate Message Passing and a Markov-Tree Prior by Subhojit Som, Philip Schniter. The abstract reads:
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.
The code and attendant example of Turbo-AMP can be found on this site.