Learned ReLU-Based Soft Thresholding: A Data-Driven Method for Non-Negative Sparse Signal Recovery

Linear Inverse Problems (LIPs) with non-negative sparse constraints on the target signal are critical in numerous applications across various fields. Among the recently proposed methods dealing with LIPs, model-based deep learning methods, particularly deep unrolling, have gained popularity due to their interpretability, efficiency, and superior performance compared to traditional iterative methods. In this work, we propose a model-driven deep learning method by unrolling the recently developed ReLU-based Hard Thresholding (RHT) algorithm for non-negative sparse signal recovery. Specifically, we employ soft thresholding activation instead of hard thresholding in the unrolling of RHT, which enhances the model performance during backpropagation. The primary advantages of the proposed Learned ReLU-based Soft Thresholding (LRST) include interpretability and faster inference after the network is trained. Our numerical experiments demonstrate that the proposed LRST outperforms its classical counterparts, showcasing its potential for more effective non-negative sparse signal recovery.