Roman Jacome;Kumar Vijay Mishra;Brian M. Sadler;Henry Arguello
{"title":"An Invitation to Hypercomplex Phase Retrieval: Theory and applications [Hypercomplex Signal and Image Processing]","authors":"Roman Jacome;Kumar Vijay Mishra;Brian M. Sadler;Henry Arguello","doi":"10.1109/MSP.2024.3394153","DOIUrl":null,"url":null,"abstract":"Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing the intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex representation of the phase retrieval (PR) problem, wherein a complex-valued signal is estimated through its intensity-only projections, has attracted significant interest. The hypercomplex PR (HPR) arises in many optical imaging and computational sensing applications that usually comprise quaternion- and octonion-valued signals. Analogous to the traditional PR, measurements in HPR may involve complex, hypercomplex, Fourier, and other sensing matrices. This set of problems opens opportunities for developing novel HSP tools and algorithms. This article provides a synopsis of the emerging areas and applications of HPR with a focus on optical imaging.","PeriodicalId":13246,"journal":{"name":"IEEE Signal Processing Magazine","volume":null,"pages":null},"PeriodicalIF":9.4000,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Signal Processing Magazine","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/10640341/","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing the intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex representation of the phase retrieval (PR) problem, wherein a complex-valued signal is estimated through its intensity-only projections, has attracted significant interest. The hypercomplex PR (HPR) arises in many optical imaging and computational sensing applications that usually comprise quaternion- and octonion-valued signals. Analogous to the traditional PR, measurements in HPR may involve complex, hypercomplex, Fourier, and other sensing matrices. This set of problems opens opportunities for developing novel HSP tools and algorithms. This article provides a synopsis of the emerging areas and applications of HPR with a focus on optical imaging.
期刊介绍:
EEE Signal Processing Magazine is a publication that focuses on signal processing research and applications. It publishes tutorial-style articles, columns, and forums that cover a wide range of topics related to signal processing. The magazine aims to provide the research, educational, and professional communities with the latest technical developments, issues, and events in the field. It serves as the main communication platform for the society, addressing important matters that concern all members.