{"title":"可伸缩框架的最小缩放","authors":"R. Domagalski, Y. Kim, S. Narayan","doi":"10.1109/SAMPTA.2015.7148857","DOIUrl":null,"url":null,"abstract":"A tight frame in R<sup>n</sup> is a redundant system which has a reconstruction formula similar to that of an orthonormal basis. For a unit-norm frame F = {f<sub>i</sub>}<sup>k</sup><sub>i=1</sub>, a scaling is a vector c = (c(l),..., c(k)) ε R<sup>k</sup>≥0 such that {c(i)f<sub>i</sub>}<sup>k</sup><sub>i=1</sub> is a tight frame in R<sup>n</sup>. If a scaling c exists, we say that F is a scalable frame. A scaling c is a minimal scaling if {fi : c{i) > 0} has no proper scalable subframes. In this paper, we present the uniqueness of the orthogonal partitioning property of any set of minimal scalings and provide a construction of scalable frames by extending the standard orthonormal basis of R<sup>n</sup>.","PeriodicalId":311830,"journal":{"name":"2015 International Conference on Sampling Theory and Applications (SampTA)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"On minimal scalings of scalable frames\",\"authors\":\"R. Domagalski, Y. Kim, S. Narayan\",\"doi\":\"10.1109/SAMPTA.2015.7148857\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A tight frame in R<sup>n</sup> is a redundant system which has a reconstruction formula similar to that of an orthonormal basis. For a unit-norm frame F = {f<sub>i</sub>}<sup>k</sup><sub>i=1</sub>, a scaling is a vector c = (c(l),..., c(k)) ε R<sup>k</sup>≥0 such that {c(i)f<sub>i</sub>}<sup>k</sup><sub>i=1</sub> is a tight frame in R<sup>n</sup>. If a scaling c exists, we say that F is a scalable frame. A scaling c is a minimal scaling if {fi : c{i) > 0} has no proper scalable subframes. In this paper, we present the uniqueness of the orthogonal partitioning property of any set of minimal scalings and provide a construction of scalable frames by extending the standard orthonormal basis of R<sup>n</sup>.\",\"PeriodicalId\":311830,\"journal\":{\"name\":\"2015 International Conference on Sampling Theory and Applications (SampTA)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-05-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 International Conference on Sampling Theory and Applications (SampTA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SAMPTA.2015.7148857\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 International Conference on Sampling Theory and Applications (SampTA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SAMPTA.2015.7148857","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A tight frame in Rn is a redundant system which has a reconstruction formula similar to that of an orthonormal basis. For a unit-norm frame F = {fi}ki=1, a scaling is a vector c = (c(l),..., c(k)) ε Rk≥0 such that {c(i)fi}ki=1 is a tight frame in Rn. If a scaling c exists, we say that F is a scalable frame. A scaling c is a minimal scaling if {fi : c{i) > 0} has no proper scalable subframes. In this paper, we present the uniqueness of the orthogonal partitioning property of any set of minimal scalings and provide a construction of scalable frames by extending the standard orthonormal basis of Rn.