%0 Journal Article
%T 稀疏信息处理中的迭代分式阈值算法<br>The iterative fraction thresholding algorithm in sparse information processing
%A 张倩
%A 李海洋&lt
%A br&gt
%A ZHANG Qian
%A LI Hai-yang
%J 山东大学学报（理学版）
%D 2017
%R 10.6040/j.issn.1671-9352.0.2017.192
%X 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。<br>Abstract: In sparse information processing, l0 minimization is often relaxed to l1 minimization to find sparse solutions. However, l1 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 thresholding algorithm(IFTA), 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
%K 收缩算子
%K 迭代阈值算法
%K 稀疏信息处理
%K 邻近算子
%K &lt
%K br&gt
%K shrinkage operator
%K proximal mapping
%K iterative thresholding algorithm
%K sparse information processing
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2017.192