Learned Two-Step Iterative Shrinkage Thresholding Algorithm for Deep Compressive Sensing

Deep unrolling architectures have revitalized compressive sensing (CS) by seamlessly blending deep neural networks with traditional optimization-based reconstruction algorithms. In pursuit of an efficient and deep interpretable approach, we propose LTwIST for CS problem, a novel deep unrolling framework that draws inspiration from the well-known two-step iterative shrinkage thresholding (TwIST) algorithm. LTwIST uses a trainable sensing matrix to adaptively learn structural information in images, and introduces a customized U-block architecture to solve the proximal mapping of nonlinear transformations connected with the sparsity-inducing regularizer. Specifically, each iteration recovery step of LTwIST corresponds to an iterative update step of the traditional TwIST algorithm. Moreover, the proposed method is designed to learn all the parameters end-to-end without manual tuning such as shrinkable thresholds, step sizes, etc. As a result, LTwIST obviates the need for manual parameter optimization, allows for high-quality image recovery and provides unambiguous interpretability. Moreover, our proposed LTwIST is also applicable to CS-based magnetic resonance imaging and exhibits a strong reconstruction performance. Extensive experiments on several public benchmark datasets demonstrate that the proposed LTwIST outperforms existing state-of-the-art deep CS methods by considerable margins in terms of quality evaluation metrics and visual performance. Our code is available on LTwIST.