Distributed Computation for Sparse Recovery via Continuous-Time Neurodynamic Approach

Sparsity has been extensively employed in multimedia sensing and computing in consumer electronics, signal and image processing, depth video codec, adaptive sparse-type equalizer, blind speech separation, and machine learning. Throughout this paper, we propose a novel distributed projection neurodynamic approach for solving the Basis Pursuit (BP) with flexible partition methods in a distributed manner. The proposed neurodynamic approach requires only that the network is undirected and connected, and no node can access the entire matrix simultaneously. First, we equivalently formulate the BP into a standard distributed optimization problem with a flexible partition-by-blocks method to obtain global information, and discuss the equivalence of their optimality conditions. Then, we propose a distributed continuous-time neurodynamic approach on the basis of primal-dual dynamical systems and projection operators, and also study its global convergence property. Finally, numerical experiments on sparse signals and image recovery further verify the effectiveness and superiority of our proposed neurodynamic approach.