Phase retrieval via Sparse Wirtinger Flow

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:355

Article

Yuan, Ziyang¹  Wang, Hongxia¹  Wang, Qi² 

[1] Natl Univ Def Technol, Dept Math, Changsha 410073, Hunan, Peoples R China

[2] Shandong Normal Univ, Coll Math & Stat, Jinan 250358, Shandong, Peoples R China

关键词: Sparse phase retrieval;    Wirtinger flow;    Gradient descent;    Hard-thresholding;   

DOI  :  10.1016/j.cam.2019.01.009

来源: Elsevier

【 摘 要 】

Phase retrieval (PR) problem is an inverse problem which arises in various applications. Based on the Wirtinger flow method, an algorithm utilizing the sparsity priority called SWF (Sparse Wirtinger Flow) is proposed in this paper to deal with the PR problem. Firstly, the support of the signal is estimated besides the initialization is evaluated based on this support. Then the evaluation is updated by the hard-thresholding method from this initialization. We prove that for any k-sparse signal with length n, SWF has a linear convergence with O(k(2)logn) phaseless Gaussian random measurements. To gets accuracy, the computational complexity of SWF is O(k(3)nlognlog1/epsilon). Numerical tests also demonstrate that SWF has a higher recovery rate than other algorithms compared especially when we have no prior information about sparsity k. Moreover, SWF is robust to the noise. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free