AMP-BCS: AMP-based image block compressed sensing with permutation of sparsified DCT coefficients

Block compressive sensing (BCS), an emerging approach for signal acquisition and reconstruction, combines high-speed sampling and compression, making it widely applicable in various imaging tasks. However, image BCS generally face the issues: challenges in accurate sampling rate allocation (SRA) and block artifact removal, and poor reconstruction algorithms. In this paper, we propose an approximate message passing (AMP)-based BCS (AMP-BCS) method. Specifically, within the sampling module, a sparsified DCT coefficient-based permutation strategy is proposed to achieve uniform energy distribution among blocks, effectively addressing the issue of SRA. Within the reconstruction module, by reweighting shallow and deep multi-scale features using several attention mechanisms, the multi-scale deep attention network (MDANet) is proposed to improve the denoising capabilities of the AMP reconstruction. Through independent sampling and joint iterative denoising, block artifacts are substantially removed. Extensive experiments demonstrate that the AMP-BCS method significantly outperforms current state-of-the-art BCS algorithms in both visual perception and objective metrics.