Deep sparse representation driven network for compressive imaging - Shi, Baoshun; Li, Dan (Knowledge-based systems, 2025)
•We propose a novel deep sparse representation model-driven network termed DeSRNet.•The local and global features are explicitly exploited to generate adaptive thresholds.•The proposed unrolled iterative method termed DUN-DeSRNet can achieve high-quality reconstructions in CI tasks.•We prove that DUN-DeSRNet can generate fixed-point convergent trajectories. In recent years, numerous compressive imaging (CI) algorithms based on deep neural networks (DNNs) have been developed and extensively explored. These algorithms capitalise the powerful representation capabilities and fast inference speeds of DNNs to achieve high-quality recovery efficiently. However, most DNN-based CI algorithms suffer from limited interpretability, hindering theoretical analysis. Multilayer convolutional sparse coding (CSC), also known as deep sparse representation (deep SR), addresses this challenge by interpreting the forward process of DNNs as a hierarchical thresholding algorithm applied to cascaded CSC layers. Nevertheless, traditional deep SR methods are computationally expensive. To overcome this limitation, we propose a deep SR-driven network (DeSRNet), which combines the interpretability of deep SR with the fast inference speed of DNNs. Specifically, DeSRNet enhances representation capability by extending single-layer SR to deep-layer SR and introduces spatially variant thresholds, computed as the product of a proportional constant vector and the input noise levels. To generate the proportional constant, we develop a feature attention network that integrates both global and local features. Additionally, DeSRNet is incorporated into a deep unfolding CI framework and evaluated on two CI tasks: spectral snapshot CI and compressed sensing magnetic resonance imaging. Experimental results show that our approach achieves competitive recovery quality compared to existing benchmark algorithms. Furthermore, we provide a theoretical convergence analysis of the proposed method.