MsDC-DEQ-Net: Deep Equilibrium Model (DEQ) with Multiscale Dilated Convolution for Image Compressive Sensing (CS)

Compressive sensing (CS) is a technique that enables the recovery of sparse signals using fewer measurements than traditional sampling methods. To address the computational challenges of CS reconstruction, our objective is to develop an interpretable and concise neural network model for reconstructing natural images using CS. We achieve this by mapping one step of the iterative shrinkage thresholding algorithm (ISTA) to a deep network block, representing one iteration of ISTA. To enhance learning ability and incorporate structural diversity, we integrate aggregated residual transformations (ResNeXt) and squeeze-and-excitation mechanisms into the ISTA block. This block serves as a deep equilibrium layer connected to a semi-tensor product network for convenient sampling and providing an initial reconstruction. The resulting model, called MsDC-DEQ-Net, exhibits competitive performance compared to state-of-the-art network-based methods. It significantly reduces storage requirements compared to deep unrolling methods, using only one iteration block instead of multiple iterations. Unlike deep unrolling models, MsDC-DEQ-Net can be iteratively used, gradually improving reconstruction accuracy while considering computation tradeoffs. Additionally, the model benefits from multiscale dilated convolutions, further enhancing performance.