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.

翻译：压缩感知（CS）是一种利用比传统采样方法更少的测量值恢复稀疏信号的技术。为解决CS重建中的计算挑战，我们旨在开发一种可解释且简洁的神经网络模型，用于通过CS重构自然图像。通过将迭代收缩阈值算法（ISTA）的一步映射到深度网络块，我们实现了ISTA的一次迭代。为增强学习能力并引入结构多样性，我们在ISTA块中集成了聚合残差变换（ResNeXt）和压缩激励（SE）机制。该块作为深度均衡层，连接到半张量积网络（STP-Net）以方便采样并提供初始重建。最终模型MsDC-DEQ-Net在与最先进的基于网络的方法相比展现出竞争性能。与深度展开方法相比，它显著减少了存储需求，仅使用一个迭代块而非多次迭代。与深度展开模型不同，MsDC-DEQ-Net可迭代使用，在考虑计算权衡的同时逐步提高重建精度。此外，该模型得益于多尺度膨胀卷积，进一步提升了性能。