Block compressed sensing images using accelerated iterative shrinkage thresholding

In this paper, first we present an improved method for conventional block-based compressed sensing (BCS) image recovery algorithm called BCS-SPL that deploys smoothed projected Landweber (SPL) iterations for image recovery. In our proposed method a median filter is applied instead of Wiener filter, specifically in low measurement rates. Also, we employ a strict thresholding criterion as an alternative to the universal threshold criterion. We refer to call our proposed method as BCS-ImSPL. Also, we investigate how the BCS-ImSPL can be improved to a faster recovery algorithm, by considering two accelerated strategies, Beck and Teboulle´s fast iterative shrinkage thresholding algorithm (FISTA) and Bioucas-Dias and Figueiredo´s two-step iterative shrinkage thresholding (TwIST) algorithm. To compare our experimental results with the other methods, we employ the pick signal to noise ratio (PSNR) and the structural similarity (SSIM) index as the quality assessors. Our vast experiments show good performance of the accelerated BCS-ImSPL method for recovery of images in terms of execution time and image quality.