A local search enhanced differential evolutionary algorithm for sparse recovery

Signal recovery problem in compressed sensing can be mathematically modeled as a ℓ0 regularized problem, which aims at searching a sparse solution. When tackling this problem, traditional mathematical approaches suffer from a limited convergence ability, especially under the noisy condition. To better solve this problem, in this paper, a novel differential evolutionary (DE) algorithm is designed to combine with a local search approach. First, an adaptive control strategy for DE is extended to recover sparse signals with noise in this paper, which is found to have a promising recovery performance. Second, in order to further enhance the convergence speed, a local search approach, i.e., a shrinkage-thresholding method (STM), is embedded into the evolutionary process of DE. Therefore, the advantages of local search capability provided by STM and global search ability of DE can be effectively combined, and resultantly a novel local search enhanced adaptive DE (named LSE-ADE) algorithm is proposed. Experimental results validate that LSE-ADE performs better than the eight classic sparse recovery algorithms and one recently proposed evolutionary algorithm, when recovering sparse signal under the noisy condition.