Reconstruction algorithm for block-based compressed sensing based on mixed variational inequality

Block compressed sensing based on mixed variational inequality (BCS-MVI) is proposed to improve the performance of current reconstruction algorithms for block-based compressed sensing. In the measurement phase, an image is sampled block by block. In the recovery period, BCS-MVI takes the sparse regularization of the natural image as prior knowledge and approaches the target function within the entire image through the modified augmented Lagrange method (ALM) and alternating direction method (ADM) of multipliers. Moreover, for the reconstruction problem including two regularization terms, an adaptive weight (-AW) strategy based on the gray entropy of the initialized image is studied. BCS-MVI achieves an average PSNR gain of 0.5-2.0 dB and an SSIM gain of 0.02-0.05 over previous block-based compressed sensing methods, and the reconstructing time only slightly fluctuates with the sampling rate. The algorithm is suitable for applications in multimedia data processing with fixed transmission delays.