{"title":"概率建模擦除的最佳对偶框架和对偶对","authors":"S. Arati, P. Devaraj, Shankhadeep Mondal","doi":"10.1007/s43036-023-00314-5","DOIUrl":null,"url":null,"abstract":"<div><p>The central focus of this paper is the analysis of optimal dual frames for a given frame as well as optimal dual pairs, in light of a probability model-based erasure during the transmission of the frame coefficients corresponding to the data. We consider these two broad and different contexts of the erasure problem and analyze each of them, with the optimality measure taken to be the spectral radius as well as the operator norm of the associated error operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal dual frames and dual pairs for probability modelled erasures\",\"authors\":\"S. Arati, P. Devaraj, Shankhadeep Mondal\",\"doi\":\"10.1007/s43036-023-00314-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The central focus of this paper is the analysis of optimal dual frames for a given frame as well as optimal dual pairs, in light of a probability model-based erasure during the transmission of the frame coefficients corresponding to the data. We consider these two broad and different contexts of the erasure problem and analyze each of them, with the optimality measure taken to be the spectral radius as well as the operator norm of the associated error operators.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"9 2\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-01-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-023-00314-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-023-00314-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Optimal dual frames and dual pairs for probability modelled erasures
The central focus of this paper is the analysis of optimal dual frames for a given frame as well as optimal dual pairs, in light of a probability model-based erasure during the transmission of the frame coefficients corresponding to the data. We consider these two broad and different contexts of the erasure problem and analyze each of them, with the optimality measure taken to be the spectral radius as well as the operator norm of the associated error operators.
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