  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 (SE) mechanisms into the ISTA block. This block serves
as a deep equilibrium layer, connected to a semi-tensor product network
(STP-Net) 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 trade-offs. Additionally, the model benefits from
multi-scale dilated convolutions, further enhancing performance.
