{"title":"三个四元数张量的同时分解及其在彩色视频信号处理中的应用","authors":"Zhuo-Heng He, Chen Chen, Xiang-Xiang Wang","doi":"10.1142/s0219530520400084","DOIUrl":null,"url":null,"abstract":"In this paper, we establish a simultaneous decomposition for three quaternion tensors via Einstein product. This simultaneous decomposition transforms the given three quaternion tensors into nice forms which have only 1 and 0. We conclude with an application in the color video signal processing. This new approach only needs to store four keys to realize the simultaneous encryption and decryption of three videos.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":"1 1","pages":"1-35"},"PeriodicalIF":2.0000,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/s0219530520400084","citationCount":"15","resultStr":"{\"title\":\"A simultaneous decomposition for three quaternion tensors with applications in color video signal processing\",\"authors\":\"Zhuo-Heng He, Chen Chen, Xiang-Xiang Wang\",\"doi\":\"10.1142/s0219530520400084\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we establish a simultaneous decomposition for three quaternion tensors via Einstein product. This simultaneous decomposition transforms the given three quaternion tensors into nice forms which have only 1 and 0. We conclude with an application in the color video signal processing. This new approach only needs to store four keys to realize the simultaneous encryption and decryption of three videos.\",\"PeriodicalId\":55519,\"journal\":{\"name\":\"Analysis and Applications\",\"volume\":\"1 1\",\"pages\":\"1-35\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2020-08-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1142/s0219530520400084\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219530520400084\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219530520400084","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
A simultaneous decomposition for three quaternion tensors with applications in color video signal processing
In this paper, we establish a simultaneous decomposition for three quaternion tensors via Einstein product. This simultaneous decomposition transforms the given three quaternion tensors into nice forms which have only 1 and 0. We conclude with an application in the color video signal processing. This new approach only needs to store four keys to realize the simultaneous encryption and decryption of three videos.
期刊介绍：
Analysis and Applications publishes high quality mathematical papers that treat those parts of analysis which have direct or potential applications to the physical and biological sciences and engineering. Some of the topics from analysis include approximation theory, asymptotic analysis, calculus of variations, integral equations, integral transforms, ordinary and partial differential equations, delay differential equations, and perturbation methods. The primary aim of the journal is to encourage the development of new techniques and results in applied analysis.
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