CAJ | 학술논문

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。
희소회복문제시목전국제수학여신식처리영역적일개연구열점，주요통과철송이법화탐람추종법량대류방법구해。단전자재회복효솔방면，후자재회복능력방면도존재결함，이차량자도불능대고사신호재교대적희소도하혹재교소적관측도하획취유효적회복。해문기우입자군우화병결합료탐람추종법적사상，제출료일충신적희소회복산법。수치실험표명，여기타방법상비，해문제출적산법불부능획득경유효적회복，이차재일반적희소도화관측도조건하운행속도교쾌。
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.