稀疏信息处理中的迭代分式阈值算法  

The iterative fraction thresholding algorithm in sparse information processing

作　　者：张倩[1] 李海洋 

机构地区：[1]西安工程大学数学系,陕西西安710048

出　　处：《山东大学学报（理学版）》2017年第9期76-82,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11271297);陕西省自然科学基金资助项目(2015JM1012);西安工程大学研究生创新基金资助项目(CX201719)

摘　　要：在稀疏信息处理中,l0范数优化问题通常转化为l1范数优化问题来求解。但l1范数优化问题存在一些不足。为寻找一种更有效的求稀疏解的算法,首先构造一个新的收缩算子,其次证明该收缩算子是某非凸函数的邻近算子。然后用该非凸函数替代l0-范数,对新的优化问题用向前-向后分裂方法得到对应的迭代阈值算法-迭代分式阈值算法(IFTA)。仿真实验表明该算法(IFTA)在稀疏信号重构和高维变量选择中均有良好的表现。In sparse information processing, 10 minimization is often relaxed to It minimization to find sparse solutions. However, lj minimization has some deficiencies. The paper aims to find a more effective algorithm to find the sparse solutions. At first, a new shrinkage operator was constructed. Secondly, this shrinkage operator was proved to be the proximal mapping of some non-convex function. Then, a new iterative thresholding algorithm, iterative fraction thresh- olding algorithm（IPTA）, was given by applying forward-backward splitting to the new optimization problem when l0- norm is replaced with this non-convex function. At last, the simulations indicate that the iterative fraction thresholding algorithm（IFTA） performs well in sparse signal reconstruction and high-dimensional variable selection.

关 键 词：稀疏信息处理 收缩算子 邻近算子 迭代阈值算法 

分 类 号：O231[理学—运筹学与控制论] O29[理学—数学]