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| 求解稀疏相位恢复问题的随机交替方向法 |
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蔡剑锋1, 焦雨领2, 吕锡亮3,4, 游俊韬1,5
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1.香港科技大学数学系, 香港 999077;2.中南财经政法大学统计与数学学院, 湖北 武汉 430073;3.武汉大学数学与统计学院;4.计算科学湖北省重点实验室, 湖北 武汉 430072;5.南方科技大学数学系, 广东 深圳 518055
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| 摘要: |
| 近年来稀疏相位恢复问题受到了越来越多的关注.本文提出了一种随机交替方法方法求解稀疏相位恢复问题，该算法采用硬阈值追踪算法求解带稀疏约束的最小二乘子问题.大量的数值实验表明，该算法可以通过O（s log n）次测量（理论上最少测量值）稳定的恢复n维s稀疏向量，并且在随机初值下可以获得全局收敛性. |
| 关键词: 相位恢复 稀疏信号 随机交替方向法 硬阈值追踪 |
| DOI： |
| 分类号:O242.1;O241.5 |
| 基金项目:The first author is partially supported by Hong Kong Research Grant Council (HKRGC) grant GRF 16306317; the second author is partially supported by National Science Foundation of China (NSFC) (11871474; 61701547); the third author is partially supported by NSFC (11871385). |
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| A STOCHASTIC ALTERNATING MINIMIZATION METHOD FOR SPARSE PHASE RETRIEVAL |
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CAI Jian-feng1, JIAO Yu-ling2, LU Xi-liang3,4, YOU Jun-tao1,5
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1.Department of Mathematics, The Hong Kong University of Science and Technology Kowloon, Hong Kong 999077, China;2.School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China;3.School of Mathematics and Statistics;4.Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China;5.Department of Mathematics, Southern University of Science and Technology, Shenzhen 518055, China
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| Abstract: |
| Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a stochastic alternating minimization method for sparse phase retrieval (StormSpar) algorithm which empirically is able to recover n-dimensional s-sparse signals from only O(s log n) measurements without a desired initial value required by many existing methods. In StormSpar, the hard-thresholding pursuit (HTP) algorithm is employed to solve the sparse constrained least-square sub-problems. The main competitive feature of StormSpar is that it converges globally requiring optimal order of number of samples with random initialization. Extensive numerical experiments are given to validate the proposed algorithm. |
| Key words: phase retrieval sparse signal stochastic alternating minimization method hard-thresholding pursuit |
