{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T06:01:12Z","timestamp":1775628072921,"version":"3.50.1"},"reference-count":37,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T00:00:00Z","timestamp":1517443200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T00:00:00Z","timestamp":1643673600000},"content-version":"vor","delay-in-days":1461,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSF grants of China","doi-asserted-by":"publisher","award":["61421062"],"award-info":[{"award-number":["61421062"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"NSF grants of China","doi-asserted-by":"publisher","award":["11471024"],"award-info":[{"award-number":["11471024"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2018,2]]},"DOI":"10.1016\/j.cam.2017.07.008","type":"journal-article","created":{"date-parts":[[2017,7,31]],"date-time":"2017-07-31T18:31:45Z","timestamp":1501525905000},"page":"202-222","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":12,"special_numbering":"C","title":["On global convergence of gradient descent algorithms for generalized phase retrieval problem"],"prefix":"10.1016","volume":"329","author":[{"given":"Ji","family":"Li","sequence":"first","affiliation":[]},{"given":"Tie","family":"Zhou","sequence":"additional","affiliation":[]},{"given":"Chao","family":"Wang","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.cam.2017.07.008_b1","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1364\/JOSAA.7.000394","article-title":"Phase retrieval in crystallography and optics","volume":"7","author":"Millane","year":"1990","journal-title":"J. Opt. Soc. Am. A"},{"issue":"1","key":"10.1016\/j.cam.2017.07.008_b2","doi-asserted-by":"crossref","first-page":"L6","DOI":"10.1088\/0022-3727\/6\/1\/102","article-title":"A method for the solution of the phase problem in electron microscopy","volume":"6","author":"Misell","year":"1973","journal-title":"J. Phys. D: Appl. Phys."},{"issue":"3","key":"10.1016\/j.cam.2017.07.008_b3","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1109\/MSP.2014.2352673","article-title":"Phase retrieval with application to optical imaging: A contemporary overview","volume":"32","author":"Shechtman","year":"2015","journal-title":"IEEE Signal Process. Mag."},{"issue":"4","key":"10.1016\/j.cam.2017.07.008_b4","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1070\/PU1988v031n04ABEH005755","article-title":"On the phase retrieval problem in optics","volume":"31","author":"Kuznetsova","year":"1988","journal-title":"Sov. Phys. Usp."},{"issue":"15","key":"10.1016\/j.cam.2017.07.008_b5","doi-asserted-by":"crossref","first-page":"2758","DOI":"10.1364\/AO.21.002758","article-title":"Phase retrieval algorithms: A comparison","volume":"21","author":"Fienup","year":"1982","journal-title":"Appl. Optim."},{"issue":"2","key":"10.1016\/j.cam.2017.07.008_b6","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1109\/TASSP.1982.1163863","article-title":"The reconstruction of a multidimensional sequence from the phase or magnitude of its fourier transform","volume":"30","author":"Hayes","year":"1982","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"issue":"2","key":"10.1016\/j.cam.2017.07.008_b7","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1109\/PROC.1982.12262","article-title":"Reducible polynomials in more than one variable","volume":"70","author":"Hayes","year":"1982","journal-title":"Proc. IEEE"},{"issue":"6","key":"10.1016\/j.cam.2017.07.008_b8","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1364\/JOSAA.20.001025","article-title":"Hybrid projection\u2013reflection method for phase retrieval","volume":"20","author":"Luke","year":"2003","journal-title":"J. Opt. Soc. Am. A"},{"issue":"1","key":"10.1016\/j.cam.2017.07.008_b9","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1088\/0266-5611\/21\/1\/004","article-title":"Relaxed averaged alternating reflections for diffraction imaging","volume":"21","author":"Luke","year":"2004","journal-title":"Inverse Problems"},{"issue":"10","key":"10.1016\/j.cam.2017.07.008_b10","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1107\/S0907444900008970","article-title":"The oversampling phasing method","volume":"56","author":"Miao","year":"2000","journal-title":"Acta Crystallogr. D"},{"issue":"1","key":"10.1016\/j.cam.2017.07.008_b11","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1364\/JOSAA.4.000118","article-title":"Reconstruction of a complex-valued object from the modulus of its fourier transform using a support constraint","volume":"4","author":"Fienup","year":"1987","journal-title":"J. Opt. Soc. Am. A"},{"issue":"7","key":"10.1016\/j.cam.2017.07.008_b12","doi-asserted-by":"crossref","first-page":"1334","DOI":"10.1364\/JOSAA.19.001334","article-title":"Phase retrieval, error reduction algorithm, and fienup variants: A view from convex optimization","volume":"19","author":"Bauschke","year":"2002","journal-title":"J. Opt. Soc. Am. A"},{"issue":"2","key":"10.1016\/j.cam.2017.07.008_b13","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1137\/151005099","article-title":"Phase retrieval via matrix completion","volume":"57","author":"Cand\u00e8s","year":"2015","journal-title":"SIAM Rev."},{"key":"10.1016\/j.cam.2017.07.008_b14","unstructured":"K. Jaganathan, Y.C. Eldar, B. Hassibi, Phase retrieval: An overview of recent developments. arXiv:1510.07713v1."},{"issue":"8","key":"10.1016\/j.cam.2017.07.008_b15","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1002\/cpa.21432","article-title":"PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming","volume":"66","author":"Cand\u00e8s","year":"2012","journal-title":"Comm. Pure Appl. Math."},{"issue":"1\u20132","key":"10.1016\/j.cam.2017.07.008_b16","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s10107-013-0738-9","article-title":"Phase recovery, maxcut and complex semidefinite programming","volume":"149","author":"Waldspurger","year":"2015","journal-title":"Math. Program."},{"key":"10.1016\/j.cam.2017.07.008_b17","unstructured":"F. Fogel, I. Waldspurger, A. d\u2019Aspremont, Phase retrieval for imaging problems. arXiv:13047735v2."},{"issue":"2","key":"10.1016\/j.cam.2017.07.008_b18","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.acha.2014.09.004","article-title":"Phase retrieval from coded diffraction patterns","volume":"39","author":"Cand\u00e8s","year":"2015","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"1","key":"10.1016\/j.cam.2017.07.008_b19","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.acha.2015.05.004","article-title":"Improved recovery guarantees for phase retrieval from coded diffraction patterns","volume":"42","author":"Gross","year":"2017","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"4","key":"10.1016\/j.cam.2017.07.008_b20","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1109\/TIT.2015.2399924","article-title":"Phase retrieval via wirtinger flow: Theory and algorithms","volume":"61","author":"Cand\u00e8s","year":"2015","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"18","key":"10.1016\/j.cam.2017.07.008_b21","doi-asserted-by":"crossref","first-page":"4814","DOI":"10.1109\/TSP.2015.2448516","article-title":"Phase retrieval using alternating minimization","volume":"63","author":"Netrapalli","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/j.cam.2017.07.008_b22","unstructured":"Y. Chen, E.J. Candes, Solving random quadratic systems of equations is nearly as easy as solving linear systems. arXiv:150505114v1."},{"key":"10.1016\/j.cam.2017.07.008_b23","unstructured":"G. Wang, G.B. Giannakis, Y.C. Eldar, Solving systems of random quadratic equations via truncated amplitude flow. arXiv:160508285v2."},{"key":"10.1016\/j.cam.2017.07.008_b24","unstructured":"P. Chen, A. Fannjiang, G.-R. Liu, Phase retrieval with one or two diffraction patterns by alternating projections of the null vector. arXiv:151007379v2."},{"key":"10.1016\/j.cam.2017.07.008_b25","series-title":"Contemporary Mathematics","doi-asserted-by":"crossref","DOI":"10.1090\/conm\/615\/12259","article-title":"Efficient algorithms for ptychographic phase retrieval","author":"Qian","year":"2014"},{"key":"10.1016\/j.cam.2017.07.008_b26","unstructured":"J. Li, T. Zhou, On relaxed averaged alternating reflections (raar) algorithm for phase retrieval from structured illuminations. arXiv:160702138v1."},{"key":"10.1016\/j.cam.2017.07.008_b27","unstructured":"J. Li, T. Zhou, Numerical optimization algorithm of wavefront phase retrieval from multiple measurements. arXiv:160701861v1."},{"key":"10.1016\/j.cam.2017.07.008_b28","unstructured":"J. Sun, Q. Qu, J. Wright, A geometric analysis of phase retrieval. arXiv:160206664v1."},{"key":"10.1016\/j.cam.2017.07.008_b29","unstructured":"K. Kreutz-Delgado, The complex gradient operator and the cr-calculus. arXiv:09064835v1."},{"key":"10.1016\/j.cam.2017.07.008_b30","series-title":"Numerical Optimization","author":"Nocedal","year":"2006"},{"issue":"3","key":"10.1016\/j.cam.2017.07.008_b31","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1137\/0720042","article-title":"The conjugate gradient method and trust regions in large scale optimization","volume":"20","author":"Steihaug","year":"1983","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"10.1016\/j.cam.2017.07.008_b32","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/s11590-008-0086-5","article-title":"Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems","volume":"3","author":"Yuan","year":"2009","journal-title":"Optim. Lett."},{"key":"10.1016\/j.cam.2017.07.008_b33","unstructured":"I. Waldspurger, Phase retrieval with random Gaussian sensing vectors by alternating projections, pp. 1\u201379. arXiv:160903088v1."},{"issue":"5","key":"10.1016\/j.cam.2017.07.008_b34","doi-asserted-by":"crossref","first-page":"3019","DOI":"10.1137\/120893707","article-title":"Sparse signal recovery from quadratic measurements via convex programming","volume":"45","author":"Li","year":"2013","journal-title":"SIAM J. Math. Anal."},{"issue":"6","key":"10.1016\/j.cam.2017.07.008_b35","doi-asserted-by":"crossref","first-page":"A3672","DOI":"10.1137\/15M1029357","article-title":"Phase retrieval from incomplete magnitude information via total variation regularization","volume":"38","author":"Chang","year":"2016","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2017.07.008_b36","unstructured":"H. Chang, Y. Lou, Y. Duan, Total variation based phase retrieval for Poisson noise removal. URL ftp:\/\/ftp.math.ucla.edu\/pub\/camreport\/cam16-76pdf."},{"key":"10.1016\/j.cam.2017.07.008_b37","unstructured":"C.D. White, S. Sanghavi, R. Ward, The local convexity of solving systems of quadratic equations. arXiv:150607868v4."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042717303497?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042717303497?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,2,1]],"date-time":"2022-02-01T03:18:18Z","timestamp":1643685498000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042717303497"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2]]},"references-count":37,"alternative-id":["S0377042717303497"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2017.07.008","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2018,2]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On global convergence of gradient descent algorithms for generalized phase retrieval problem","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2017.07.008","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2017 Elsevier B.V.","name":"copyright","label":"Copyright"}]}}