FISTA-CSNet: a deep compressed sensing network by unrolling iterative optimization algorithm

In order to fast sample an image and accurately reconstruct the image from a small amount of sampled data, we design a novel deep network for optimization-based algorithm mapping to efficiently tackle the problem of image compressed sensing (CS). The new deep network structure, dubbed FISTA-CSNet, unrolls the fast iterative shrinkage-thresholding algorithm (FISTA) into two modules: sampling matrix module and reconstruction network module. The two modules are optimized jointly and the parameters in the matrix and network are discriminatively learned by end-to-end training. The sampling matrix is adaptively learned from the training images, which can better utilize the image texture information for CS reconstruction. The reconstruction network module is subdivided into two parts. The first part casts the optimization-based algorithm into deep network form and the second part uses a set of convolutional filters and nonlinear activation function to reduce the blocking artifacts introduced by block CS. In view of the unavailability of the reconstruction network at different sampling ratios, the ratio-adaptive sampling matrix and the reconstruction network are proposed to realize the multi-sampling ratio reuse version of FISTA-CSNet, dubbed FISTA-CSNet*, so that the system can operate on a range of sampling ratios. Extensive experiments show that the proposed FISTA-CSNets outperform previous state-of-the-art CS methods in term of PSNR, SSIM, FSIM and visual quality.