  The learned denoising-based approximate message passing (LDAMP) algorithm has
attracted great attention for image compressed sensing (CS) tasks. However, it
has two issues: first, its global measurement model severely restricts its
applicability to high-dimensional images, and its block-based measurement
method exhibits obvious block artifacts; second, the denoiser in the LDAMP is
too simple, and existing denoisers have limited ability in detail recovery. In
this paper, to overcome the issues and develop a high-performance LDAMP method
for image block compressed sensing (BCS), we propose a novel sparsity and
coefficient permutation-based AMP (SCP-AMP) method consisting of the
block-based sampling and the two-domain reconstruction modules. In the sampling
module, SCP-AMP adopts a discrete cosine transform (DCT) based sparsity
strategy to reduce the impact of the high-frequency coefficient on the
reconstruction, followed by a coefficient permutation strategy to avoid block
artifacts. In the reconstruction module, a two-domain AMP method with DCT
domain noise correction and pixel domain denoising is proposed for iterative
reconstruction. Regarding the denoiser, we proposed a multi-level deep
attention network (MDANet) to enhance the texture details by employing
multi-level features and multiple attention mechanisms. Extensive experiments
demonstrated that the proposed SCP-AMP method achieved better reconstruction
accuracy than other state-of-the-art BCS algorithms in terms of both visual
perception and objective metrics.

Computer Vision and Pattern Recognition;Multimedia;Image and Video Processing