  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.
