@article{969f8b0226b54e0193e2cab13ce51750,
title = "Phase retrieval by linear algebra",
abstract = "The null vector method, based on a simple linear algebraic concept, is proposed as an initialization method for nonconvex approaches to the phase retrieval problem. For the stylized measurement with random complex Gaussian matrices, a nonasymptotic error bound is derived, stronger than that of the spectral vector method. Numerical experiments show that the null vector method also has a superior performance for the realistic measurement of coded diffraction patterns in coherent diffractive imaging.",
author = "Pengwen Chen and Albert Fannjiang and Liu, {Gi Ren}",
note = "Funding Information: ∗Received by the editors December 13, 2016; accepted for publication (in revised form) by J. Tropp June 12, 2017; published electronically August 17, 2017. http://www.siam.org/journals/simax/38-3/M110774.html Funding: The work of the first author was supported in part by grant 103-2115-M-005-006-MY2 from the Ministry of Science and Technology, Taiwan, and U.S. NIH grant U01-HL-114494. The work of the second author was supported in part by U.S. National Science Foundation grant DMS-1413373 and Simons Foundation grant 275037. †Department of Applied Mathematics, National Chung Hsing University, Taichung, Taiwan (pengwen@nchu.edu.tw). ‡Corresponding author. Department of Mathematics, University of California, Davis, CA 95616 (fannjiang@math.ucdavis.edu). §Department of Mathematics, National Cheng Kung University, Tainan, Taiwan (girenliu@mail. ncku.edu.tw).",
year = "2017",
doi = "10.1137/16M1107747",
language = "English",
volume = "38",
pages = "854--868",
journal = "SIAM Journal on Matrix Analysis and Applications",
issn = "0895-4798",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}