{"title":"作为L/sub 1/-范数正则化器的数字滤波器","authors":"S. Alliney","doi":"10.1109/MDSP.1989.97057","DOIUrl":null,"url":null,"abstract":"Summary form only given. It is observed that classical filtering theory (both in 1-D and 2-D cases) can be viewed as a particular solution to the minimum problem for a certain Tikhonov functional and that the underlying functional setting is strongly related to Sobolev space theory. The author is attempting to generalize that approach by considering Tikhonov functionals of a particular type, defined over discrete signals in terms of the L/sub 1/-norm.<<ETX>>","PeriodicalId":340681,"journal":{"name":"Sixth Multidimensional Signal Processing Workshop,","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1989-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Digital filters as L/sub 1/-norm regularizers\",\"authors\":\"S. Alliney\",\"doi\":\"10.1109/MDSP.1989.97057\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary form only given. It is observed that classical filtering theory (both in 1-D and 2-D cases) can be viewed as a particular solution to the minimum problem for a certain Tikhonov functional and that the underlying functional setting is strongly related to Sobolev space theory. The author is attempting to generalize that approach by considering Tikhonov functionals of a particular type, defined over discrete signals in terms of the L/sub 1/-norm.<<ETX>>\",\"PeriodicalId\":340681,\"journal\":{\"name\":\"Sixth Multidimensional Signal Processing Workshop,\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Sixth Multidimensional Signal Processing Workshop,\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MDSP.1989.97057\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sixth Multidimensional Signal Processing Workshop,","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MDSP.1989.97057","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Summary form only given. It is observed that classical filtering theory (both in 1-D and 2-D cases) can be viewed as a particular solution to the minimum problem for a certain Tikhonov functional and that the underlying functional setting is strongly related to Sobolev space theory. The author is attempting to generalize that approach by considering Tikhonov functionals of a particular type, defined over discrete signals in terms of the L/sub 1/-norm.<>
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