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Compressive sensing (CS) is a technique that enables the recovery of sparsesignals using fewer measurements than traditional sampling methods. To addressthe computational challenges of CS reconstruction, our objective is to developan interpretable and concise neural network model for reconstructing naturalimages using CS. We achieve this by mapping one step of the iterative shrinkagethresholding algorithm (ISTA) to a deep network block, representing oneiteration of ISTA. To enhance learning ability and incorporate structuraldiversity, we integrate aggregated residual transformations (ResNeXt) andsqueeze-and-excitation (SE) mechanisms into the ISTA block. This block servesas a deep equilibrium layer, connected to a semi-tensor product network(STP-Net) for convenient sampling and providing an initial reconstruction. Theresulting model, called MsDC-DEQ-Net, exhibits competitive performance comparedto state-of-the-art network-based methods. It significantly reduces storagerequirements compared to deep unrolling methods, using only one iteration blockinstead of multiple iterations. Unlike deep unrolling models, MsDC-DEQ-Net canbe iteratively used, gradually improving reconstruction accuracy whileconsidering computation trade-offs. Additionally, the model benefits frommulti-scale dilated convolutions, further enhancing performance.

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