ISTA-Net: Iterative Shrinkage-Thresholding Algorithm Inspired Deep Network for Image Compressive Sensing

Traditional methods for image compressive sensing (CS) reconstruction solve a welldefined inverse problem (convex optimization problems in many cases) that is based on a predefined CS model, which defines the underlying structure of the problem and is generally solved by employing convergent iterative solvers. These optimization-based CS methods face the challenge of choosing optimal transforms and tuning parameters in their solvers, while also suffering from high computational complexity in most cases. Recently, some deep network based CS algorithms have been proposed to improve CS reconstruction performance, while dramatically reducing time complexity as compared to optimization-based methods. Despite their impressive results, the proposed networks (either with fully-connected or repetitive convolutional layers) lack any structural diversity and they are trained as a black box, void of any insights from the CS domain. In this paper, we combine the merits of both types of CS methods: the structure insights of optimization-based method and the performance/speed of network-based ones. We propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general l1 norm CS reconstruction model. ISTA-Net essentially implements a truncated form of ISTA, where all ISTA-Net parameters (e.g. transforms, shrinkage thresholds, step size, etc.), are learned end-to-end to minimize a reconstruction error in training. Borrowing more insights from the optimization realm, we propose an accelerated version of ISTANet, dubbed FISTA-Net, which is inspired by the fast iterative shrinkage-thresholding algorithm (FISTA). Interestingly, this acceleration naturally leads to skip connections in the underlying network design. Extensive CS experiments demonstrate that the proposed ISTA-Net and FISTA-Net outperform existing optimization-based and network-based CS methods by large margins, while maintaining a fast runtime with 20 fps on a Quadro 6000 GPU.