Block compressed sensing images using Curvelet transform

Due to the optimal sparse representation of objects with edges by the multiscale and directional Curvelet Transform, its application have been increasingly interested over the past years. In this paper, we investigate how the block-based compressed sensing (BCS) can be improved to an efficient recovery algorithm, by employing the iterative Curvelet thresholding (ICT). Also, we consider two accelerated iterative shrinkage thresholding (IST) methods, including the following: 1) Beck and Teboulle´s fast iterative shrinkage thresholding algorithm (FISTA); 2) Bioucas-Dias and Figueiredo´s two-step iterative shrinkage thresholding (TwIST) algorithm, to increase the execution speed of the proposed methods rather than simple ICT. To compare our experimental results with the results of some other methods, we employ pick signal to noise ratio (PSNR) and structural similarity (SSIM) index as the quality assessor. Numerical results show good performance of the new proposed BCS using accelerated ICT methods, in terms of these two quality assessments.