STP-DEQ-Net: A Deep Equilibrium Model Based on ISTA Method for Image Compressive Sensing

With the aim of finding a compact and efficient model for compressive sensing (CS) imaging, we sample images based on semi-tensor product (STP) and design a deep equilibrium (DEQ) neural network. We measure the images and produce their initial reconstruction with STP method. The results can be refined by deep unrolling methods (DUMs) which use architectures borrow insights from iterations of an optimization method. Though DUMs have well-defined interpretability, a few iterations will make the model takes up huge memory space. It is difficult for training and application. Inspired by the iterative shrinkage-thresholding algorithm (ISTA) and deep equilibrium architecture, we build a deep network dubbed as STP-DEQ-Net. It reduces the storage of the system from multiple ISTA iteration blocks to only one block. The experiments show that the proposed method operates with attractive performance compared with competing methods. The trained model has trade-offs between reconstruction quality and computation.