一种基于粒子群优化的稀疏恢复算法

A Sparse Recovery Algorithm Based on Particle Swarm Optimization

稀疏恢复问题是目前国际数学与信息处理领域的一个研究热点,主要通过凸松弛法和贪婪追踪法两大类方法求解。但前者在恢复效率方面,后者在恢复能力方面都存在缺陷,而且两者都不能对高斯信号在较大的稀疏度下或在较小的观测度下获取有效的恢复。该文基于粒子群优化并结合了贪婪追踪法的思想,提出了一种新的稀疏恢复算法。数值实验表明,与其它方法相比,该文提出的算法不仅能获得更有效的恢复,而且在一般的稀疏度和观测度条件下运行速度较快。

Sparse recovery is a hot topic around the areas of international mathematics and information processing at present, and it is mainly solved by two major strategies including convex relaxation methods and greedy pursuit methods. However, considering the former on efficiency and the latter on ability, they own shortcomings respectively, and neither can recover Gaussian signals with large sparsity level or small measurement level effectively. In this paper, a new sparse recovery algorithm propose is proposed and based on particle swarm optimization combining with the thought of greedy pursuit methods. It is demonstrated by a series of numerical simulations that when compared to other methods, the proposed algorithm could not only achieve better recovery performance, but also runs relatively fast when recovering Gaussian signals with normal sparsity level or normal measurement level.