Better and faster, when ADMM meets CNN: Compressive-sensed image reconstruction

Compressive sensing (CS) has drawn enormous amount of attention in recent years owing to its sub-Nyquist sampling rate and low-complexity requirement at the encoder. However, it turns out that the decoder in lieu of the encoder suffers from heavy computation in order to decently recover the signal from its CS measurements. Inspired by the recent success of deep learning in low-level computer vision problems, in this paper, we propose a solution that utilizes deep convolutional neural network (CNN) to recover image signals from CS measurements effectively and efficiently. Rather than training a neural network from scratch that inputs CS measurements and outputs images, we incorporate an off-the-shelf CNN model into the CS reconstruction framework even without the effort of finetuning. To this end, we formulate the CS recovery problem into two subproblems via the alternate direction method of multiplers (ADMM): a convex quadratic problem and an image denoising problem, in which CNN has exhibited its desirable reconstruction performance and low computational complexity. Hereby, powerful GPU could be utilized to speed up the reconstruction. Experiments demonstrate that our proposed CS image reconstruction solution surpasses state-of-the-art CS models by a significant margin in speed and performance.