A structured AMP method recovering signals with a forward-backward splitting mode

D-AMP (Denoising-based Approximate Message Passing) method usually offers an efficient recovery in image Compressive Sensing (CS). To apply D-AMP in structured signals, we focus on a forward-backward splitting mode [5] and have to deal with signal bias in the backward shrinkage step. For deviation calibrating and better adaptation to structure clustering, we modify the BM3D (Block-matching and 3D filtering) based D-AMP method (named as BM3D-AMP) in two folds: 1) Iteratively optimize a data-fidelity term with total variation (TV) and wavelet sparse constraints, aiming to diminish the bias resulted from the splitting operation. 2) Suggest a more accurate initial-state estimation by using a sparse tree and finally accelerate the CS reconstruction. Experimental results show that the proposed algorithm averagely achieves higher PSNR values than the BM3D-AMP algorithm.