{"title":"块稀疏压缩感知中混合l2 / l1范数最小化的相变","authors":"Toshiyuki Tanaka","doi":"10.1109/ISIT.2019.8849798","DOIUrl":null,"url":null,"abstract":"We have evaluated, via the replica method, phase transition thresholds for the mixed ℓ2/ℓ1-norm minimization applied to block-sparse compressed sensing with randomly generated measurement matrices. Our analysis takes into account that the matrix elements may be of non-zero mean, and shows that the phase transition threshold for the mixed ℓ2/ℓ1-norm minimization improves when the matrix elements have non-zero mean and the distribution of non-zero blocks of the target vector to be estimated has a certain imbalance.","PeriodicalId":6708,"journal":{"name":"2019 IEEE International Symposium on Information Theory (ISIT)","volume":"124 1","pages":"2848-2852"},"PeriodicalIF":0.0000,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Phase Transition in Mixed ℓ2/ℓ1-norm Minimization for Block-Sparse Compressed Sensing\",\"authors\":\"Toshiyuki Tanaka\",\"doi\":\"10.1109/ISIT.2019.8849798\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We have evaluated, via the replica method, phase transition thresholds for the mixed ℓ2/ℓ1-norm minimization applied to block-sparse compressed sensing with randomly generated measurement matrices. Our analysis takes into account that the matrix elements may be of non-zero mean, and shows that the phase transition threshold for the mixed ℓ2/ℓ1-norm minimization improves when the matrix elements have non-zero mean and the distribution of non-zero blocks of the target vector to be estimated has a certain imbalance.\",\"PeriodicalId\":6708,\"journal\":{\"name\":\"2019 IEEE International Symposium on Information Theory (ISIT)\",\"volume\":\"124 1\",\"pages\":\"2848-2852\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2019 IEEE International Symposium on Information Theory (ISIT)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2019.8849798\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 IEEE International Symposium on Information Theory (ISIT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2019.8849798","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Phase Transition in Mixed ℓ2/ℓ1-norm Minimization for Block-Sparse Compressed Sensing
We have evaluated, via the replica method, phase transition thresholds for the mixed ℓ2/ℓ1-norm minimization applied to block-sparse compressed sensing with randomly generated measurement matrices. Our analysis takes into account that the matrix elements may be of non-zero mean, and shows that the phase transition threshold for the mixed ℓ2/ℓ1-norm minimization improves when the matrix elements have non-zero mean and the distribution of non-zero blocks of the target vector to be estimated has a certain imbalance.
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