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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (9): 76-82.doi: 10.6040/j.issn.1671-9352.0.2017.192

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稀疏信息处理中的迭代分式阈值算法

张倩,李海洋*   

  1. 西安工程大学数学系, 陕西 西安 710048
  • 收稿日期:2017-04-24 出版日期:2017-09-20 发布日期:2017-09-15
  • 通讯作者: 李海洋(1975— ), 男, 博士后, 副教授, 研究方向为稀疏信息处理、机器学习. E-mail:fplihaiyang@126.com E-mail:2478867382@qq.com
  • 作者简介:张倩(1994— ),女,硕士研究生,研究方向为稀疏信息处理. E-mail:2478867382@qq.com
  • 基金资助:
    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)

The iterative fraction thresholding algorithm in sparse information processing

ZHANG Qian, LI Hai-yang*   

  1. Department of Mathematics, Xian Polytechnic University, Xian 710048, Shaanxi, China
  • Received:2017-04-24 Online:2017-09-20 Published:2017-09-15

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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。

关键词: 收缩算子, 迭代阈值算法, 稀疏信息处理, 邻近算子

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.

Key words: shrinkage operator, proximal mapping, iterative thresholding algorithm, sparse information processing

中图分类号: 

  • O231
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