Nonzero Degree-Based Multiobjective Cooperative Coevolutionary for Block Sparse Recovery

Abstract

Block sparse signals have the characteristics of nonzero values concentrated as blocks. Therefore, block sparse recovery requires recovering the original signal from the observed signal and the measurement matrix, where the recovered error should be small and the signal satisfies the block sparsity. In this paper, block sparse recovery is solved as a multiobjective problem (MOP) and the recovery error, sparsity, and the block number of the recovered signal are considered as the conflicting objectives. Furthermore, the dimensionality of real block sparse signals is often too large, which increases the difficulty of recovery. Cooperative coevolutionary (CC) can effectively alleviate the curse of dimensionality in block sparse recovery. In addition, block sparsity causes zero and nonzero variables in the signal to form natural clusters, which is similar to the decomposition and cooperation of subproblems in CC. Therefore, CC is used in the algorithm to solve the block sparse MOP and decomposes the original problem into different subproblems. Each subproblem has a defined nonzero degree that can be combined with the proposed adaptive operator to adaptively adjust the way of generating new solutions of subproblem, which encourages the complete solution to have block sparsity. For the increased number of function evaluations (FEs) caused by the decomposition, a new list-inquiry evaluation is designed to avoid repeated evaluation. Finally, the experimental results on simulated data and real data have demonstrated the effectiveness of the proposed algorithm.