{"title":"基于卷积希尔伯特空间的相位检索算法","authors":"A. Cetin, R. Ansari","doi":"10.1364/srs.1986.pd2","DOIUrl":null,"url":null,"abstract":"A phase retrieval algorithm using the method of projection onto convex sets (POCS) [1,2] in a new Hilbert Space framework which is based on convolution is described. In this space, the set of sequences with a prescribed Fourier Transform magnitude constitute a closed convex set, which is not true in (or L2) Hilbert space. This property of the constraints ensures convergence in the POCS method. Examples of phase retrieval for 2-D sequences are presented.","PeriodicalId":262149,"journal":{"name":"Topical Meeting On Signal Recovery and Synthesis II","volume":"126 16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Phase Retrieval Algorithm Using a Convolution Based Hilbert Space\",\"authors\":\"A. Cetin, R. Ansari\",\"doi\":\"10.1364/srs.1986.pd2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A phase retrieval algorithm using the method of projection onto convex sets (POCS) [1,2] in a new Hilbert Space framework which is based on convolution is described. In this space, the set of sequences with a prescribed Fourier Transform magnitude constitute a closed convex set, which is not true in (or L2) Hilbert space. This property of the constraints ensures convergence in the POCS method. Examples of phase retrieval for 2-D sequences are presented.\",\"PeriodicalId\":262149,\"journal\":{\"name\":\"Topical Meeting On Signal Recovery and Synthesis II\",\"volume\":\"126 16 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topical Meeting On Signal Recovery and Synthesis II\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1364/srs.1986.pd2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topical Meeting On Signal Recovery and Synthesis II","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1364/srs.1986.pd2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Phase Retrieval Algorithm Using a Convolution Based Hilbert Space
A phase retrieval algorithm using the method of projection onto convex sets (POCS) [1,2] in a new Hilbert Space framework which is based on convolution is described. In this space, the set of sequences with a prescribed Fourier Transform magnitude constitute a closed convex set, which is not true in (or L2) Hilbert space. This property of the constraints ensures convergence in the POCS method. Examples of phase retrieval for 2-D sequences are presented.
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