A Composite Initialization Method for Phase Retrieval

• Published in: Symmetry (Basel) Vol. 13; no. 11; p. 2006
• Main Authors: Luo, Qi, Lin, Shijian, Wang, Hongxia
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.11.2021
• Subjects: Algorithms; Eigenvalues; Fourier transforms; Inverse problems; Mathematical analysis; Methods; non-convex reconstruction; Phase retrieval; spectral method
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym13112006

Phase retrieval is a classical inverse problem with respect to recovering a signal from a system of phaseless constraints. Many recently proposed methods for phase retrieval such as PhaseMax and gradient-descent algorithms enjoy benign theoretical guarantees on the condition that an elaborate estimate of true solution is provided. Current initialization methods do not perform well when number of measurements are low, which deteriorates the success rate of current phase retrieval methods. We propose a new initialization method that can obtain an estimate of the original signal with uniformly higher accuracy which combines the advantages of the null vector method and maximal correlation method. The constructed spectral matrix for the proposed initialization method has a simple and symmetrical form. A lower error bound is proved theoretically as well as verified numerically.