Nest-MGDL: Nesterov-Optimized Memory and Geometric Distillation Learning for Image Compressed Sensing

Compressed sensing (CS) reconstruction is a powerful technique for image compression and reconstruction. Most existing deep learning and deep unfolding reconstruction methods: 1) do not sufficiently analyze the proximal subproblem and naturally derive network architectures from mathematical theory; 2) lack the ability to correct errors and recover details via multi-domain, multi-scale and multi-resolution analysis; 3) depend only on the previous stage and overlooking valuable information from earlier stages. In this study, we propose a Nesterov-optimized memory and geometric distillation learning framework (Nest-MGDL), which effectively integrates interpretability and adaptability to achieve robust and generalizable deep learning performance. By reformulating the proximal subproblem as the decomposition and distillation of memory and geometric priors across diverse domains, and integrating a local multi-level feature aggregation strategy, Nest-MGDL enables theoretically grounded network design and accurate multi-scale correction of errors. Inspired by the third-Nesterov acceleration scheme with fast convergence, we incorporate gradient information from measurement errors across multiple historical stages to achieve more consistent and accurate reconstruction. It provides new insights into leveraging historical measurement errors and designing explainable network architectures. All parameters in our Nest-MGDL are learnable end-to-end with adaptive initialization, enhancing model flexibility and ensuring stable convergence. Extensive experiments show that Nest-MGDL outperforms other state-of-the-art methods.