Non-negative sparse signal recovery using the integration of ReLU and hard thresholding pursuit operators

Linear inverse problems involving non-negative sparse approximations are essential in various applications such as face recognition, DNA microarrays, and spectral unmixing. Recent advancements in ReLU-based algorithms, such as ReLU-based hard thresholding (RHT) and momentum-boosted adaptive thresholding (MBAT), solve this problem by leveraging the rectified linear unit (ReLU) in combination with thresholding operators to produce non-negative sparse solutions. Despite these developments, challenges persist in achieving high recovery performance and faster convergence. To address these issues, we propose a novel ReLU-based algorithm for non-negative sparse signal recovery, termed ReLU-based hard thresholding pursuit (RHTP). Specifically, RHTP integrates the ReLU within the hard thresholding pursuit framework to enable efficient recovery of non-negative sparse signals. We derive sufficient criteria for ensuring the stable recovery of sparse signals generated from RHTP based on the restricted isometry property. Additionally, we provide a theoretical analysis showing that the RHTP algorithm converges more rapidly than the RHT algorithm. Numerical experiments demonstrate that RHTP outperforms existing algorithms in recovering binary sparse signals and delivers comparable performance to the state-of-the-art MBAT algorithm in recovering non-negative sparse Gaussian signals. Furthermore, empirical results demonstrate that RHTP exhibits faster convergence compared to other methods. Moreover, RHTP achieves higher classification accuracy than other non-negative sparse signal recovery algorithms on the Yale Face dataset, demonstrating its effectiveness in face recognition.