一种改进的迭代软阈值算法及其应用  

An improved iterative soft thresholding algorithm and application

作　　者：张倩[1] 李海洋[1] ZHANG Qian;LI Haiyang(School of Science,Xi′an Polytechnic University,Xi′an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2018年第2期253-260,共8页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11271297);陕西省自然科学基金(2015TM1012);西安工程大学研究生创新基金(CX201719)

摘　　要：为了解决迭代软阈值算法(ISTA)收敛速度较慢,得到的最优解不够稀疏等问题,提出基于梯度算法思想的改进ISTA,即SFISTA.该算法修改了ISTA迭代式中的梯度算子,使得迭代点x^(n+1)的求解同时依赖于前两步的迭代.将SFISTA应用于稀疏信号处理及稀疏主成分分析实验中,结果表明,该算法不仅提高了ISTA的收敛速度,也促进了最优解的稀疏度.In order to solve the problems of the iterative soft thresholding algorithm(ISTA)that convergence rate is slow and the obtained optimal solution is not enough sparse,an improved algorithm called SFISTA based on the gradient algorithm is proposed.The algorithm modifies the gradient operator in the ISTA iterative method,so that the solution of the iterative point x n+1 depends on the iteration of the first two steps.Applying SFISTA to sparse signal processing and sparse principal component analysis,the experimental results show that the new algorithm not only can improve the convergence rate of ISTA,but can also promote the sparsity of the optimal solution.

关 键 词：迭代软阈值算法 梯度算子 稀疏信号处理 稀疏主成分 

分 类 号：O231[理学—运筹学与控制论] O29[理学—数学]