{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:54:17Z","timestamp":1767707657882,"version":"3.41.2"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100017596","name":"Natural Science Basic Research Program of Shaanxi Province","doi-asserted-by":"publisher","award":["2021JM-399"],"award-info":[{"award-number":["2021JM-399"]}],"id":[{"id":"10.13039\/501100017596","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant No.11901192"],"award-info":[{"award-number":["Grant No.11901192"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p> The phase retrieval (PR) problem is to reconstruct real\/complex functions from the magnitudes of their Fourier\/frame measurements in classical computational imaging. In this paper, we consider phase retrieval of complex vectors\/images from the magnitudes of short-time fractional Fourier transform (STFrFT). In our setting, the above problem is solved by minimizing a least square ReLu loss function and a novel algorithm by alternating direction method of multipliers (ADMM) is presented. As shown in the numerical simulations on complex signals\/images, our proposed PR-ADMM algorithm from STFrFT has a better recovery performance with flexible window functions and appropriate fractional orders. It demonstrates to have satisfactory performance from mixed phaseless STFrFT measurements. Compared with several six other main algorithms, the proposed algorithm explicitly recovers the phase of image with higher the peak signal-to-noise ratio. Meanwhile, the proposed algorithm is robust to noise. These also generalize some of about phase retrievals with Fourier measurements. <\/jats:p>","DOI":"10.1142\/s0219691323500157","type":"journal-article","created":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T14:22:50Z","timestamp":1677680570000},"source":"Crossref","is-referenced-by-count":1,"title":["Phase retrieval from short-time fractional Fourier measurements using alternating direction method of multipliers"],"prefix":"10.1142","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2354-3716","authenticated-orcid":false,"given":"Lan","family":"Li","sequence":"first","affiliation":[{"name":"School of Science, Xi\u2019an Shiyou University, Xi\u2019an 710065, Shaanxi, P. R. China"}]},{"given":"Lu","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an Shiyou University, Xi\u2019an 710065, Shaanxi, P. R. China"}]},{"given":"Mingli","family":"Jing","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an Shiyou University, Xi\u2019an 710065, Shaanxi, P. R. China"}]},{"given":"Wei","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an Shiyou University, Xi\u2019an 710065, Shaanxi, P. R. China"}]},{"given":"Yang","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, P. R. 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