Distributed Projection Neurodynamic Approaches in Continuous and Discrete Time for BP With Block Decomposition of Measurement Matrix.

Abstract

Aiming at the situation where the measurement matrix B has a flexible block decomposition, this article designs two novel distributed continuous- and discrete-time projection neurodynamic approaches to solve the basis pursuit (BP) problem for sparse recovery. These approaches only require information from each flexible block of the measurement matrix B, rather than from each row, column, or the entire matrix. First, with the aid of the primal-dual dynamical approach, projection operator, and second-order multiagent consensus condition, a novel distributed projection neurodynamic approach in continuous time (DPNA-CT-B) is proposed, and its optimality and global asymptotic stability are rigorously proved. Moreover, based on the forward and backward Euler methods and variable substitution methods, a corresponding distributed projection neurodynamic approach in discrete time (DPNA-DT-B) is designed. Finally, through sparse signal and image reconstruction experiments, the effectiveness and superiority of the proposed neurodynamic approaches are verified.