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.

Closed-loop architecture is widely utilized in automatic control systems and attain distinguished performance. However, classical compressive sensing systems employ open-loop architecture with separated sampling and reconstruction units. Therefore, a method of iterative compensation recovery for image compressive sensing (ICRICS) is proposed by introducing closed-loop framework into traditional compresses sensing systems. The proposed method depends on any existing approaches and upgrades their reconstruction performance by adding negative feedback structure. Theory analysis on negative feedback of compressive sensing systems is performed. An approximate mathematical proof of the effectiveness of the proposed method is also provided. Simulation experiments on more than 3 image datasets show that the proposed method is superior to 10 competition approaches in reconstruction performance. The maximum increment of average peak signal-to-noise ratio is 4.36 dB and the maximum increment of average structural similarity is 0.034 on one dataset. The proposed method based on negative feedback mechanism can efficiently correct the recovery error in the existing systems of image compressive sensing.