{"title":"关于完全对称等斜紧融合框架的一个注记","authors":"M. Fickus, Joseph W. Iverson, J. Jasper, D. Mixon","doi":"10.1109/icassp43922.2022.9746835","DOIUrl":null,"url":null,"abstract":"Consider the fundamental problem of arranging r-dimensional subspaces of Rd in such a way that maximizes the minimum distance between unit vectors in different subspaces. It is well known that equi-isoclinic tight fusion frames (EITFFs) are optimal for this packing problem, but such ensembles are notoriously hard to construct. In this paper, we present a novel construction of EITFFs that are totally symmetric: any permutation of the subspaces can be realized by an orthogonal transformation of ℝd.","PeriodicalId":272439,"journal":{"name":"ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A Note on Totally Symmetric Equi-Isoclinic Tight Fusion Frames\",\"authors\":\"M. Fickus, Joseph W. Iverson, J. Jasper, D. Mixon\",\"doi\":\"10.1109/icassp43922.2022.9746835\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consider the fundamental problem of arranging r-dimensional subspaces of Rd in such a way that maximizes the minimum distance between unit vectors in different subspaces. It is well known that equi-isoclinic tight fusion frames (EITFFs) are optimal for this packing problem, but such ensembles are notoriously hard to construct. In this paper, we present a novel construction of EITFFs that are totally symmetric: any permutation of the subspaces can be realized by an orthogonal transformation of ℝd.\",\"PeriodicalId\":272439,\"journal\":{\"name\":\"ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-05-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/icassp43922.2022.9746835\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/icassp43922.2022.9746835","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Note on Totally Symmetric Equi-Isoclinic Tight Fusion Frames
Consider the fundamental problem of arranging r-dimensional subspaces of Rd in such a way that maximizes the minimum distance between unit vectors in different subspaces. It is well known that equi-isoclinic tight fusion frames (EITFFs) are optimal for this packing problem, but such ensembles are notoriously hard to construct. In this paper, we present a novel construction of EITFFs that are totally symmetric: any permutation of the subspaces can be realized by an orthogonal transformation of ℝd.
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