A Distributed Projection Neurodynamic Approach for Solving BP Denoising Problem in Sparse Recovery

This paper investigates a novel projection neurodynamic approach for solving the basis pursuit denoising (BPDN) in a distributed manner. First, by using the distributed consensus theorem over undirected graph and supplementary variables method, the distributed version of BPDN is obtained. Second, with the help of projection operators, primal-dual dynamical system and derivative feedback terms, a novel distributed neurodynamic approach is proposed to deal with the distributed version of BPDN for sparse recovery. Moreover, the optimality and convergence properties of the proposed distributed projection neurodynamic approach (DPNA) are analyzed rigorously. Finally, we apply DPNA to sparse signal reconstruction which demonstrates the effectiveness of DPNA through numerical experiments. In addition, inspired by the role of image reconstruction technology in the field of defense against adversarial attack, we use DPNA as a preprocessing method to enhance the robustness of the deep model. Compared with known defense schemes such as JEPG, ComDefend, and OMP, our DPNA is better than them.