{"title":"消失矩和最小滤波范数小波及其在图像压缩中的应用","authors":"Zhuhan Jiang, Xiling Guo","doi":"10.1109/ISSPA.2001.949787","DOIUrl":null,"url":null,"abstract":"Wavelet systems of a maximum number of balanced vanishing moments are known to be extremely useful in a variety of applications including image and video compression. J. Tian and R.O. Wells Jr (see \"Vanishing moments and biorthogonal wavelet systems\", Mathematics in Signal Processing IV, Oxford University Press, 1997) recently created a family of such wavelet systems, called the biorthogonal Coifman wavelets, which proved valuable in both mathematics and applications. We first present an extension of Tian and Wells' family of biorthogonal Coifman wavelets by recovering other \"missing\" members of the biorthogonal Coifman wavelet systems. We then propose and study the wavelet filters of the minimal synthesis norm. It is also demonstrated that an additional feature of the minimal norm will in general improve the compression performance of the codecs based on such wavelets.","PeriodicalId":236050,"journal":{"name":"Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Wavelets of vanishing moments and minimal filter norms and the application to image compression\",\"authors\":\"Zhuhan Jiang, Xiling Guo\",\"doi\":\"10.1109/ISSPA.2001.949787\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Wavelet systems of a maximum number of balanced vanishing moments are known to be extremely useful in a variety of applications including image and video compression. J. Tian and R.O. Wells Jr (see \\\"Vanishing moments and biorthogonal wavelet systems\\\", Mathematics in Signal Processing IV, Oxford University Press, 1997) recently created a family of such wavelet systems, called the biorthogonal Coifman wavelets, which proved valuable in both mathematics and applications. We first present an extension of Tian and Wells' family of biorthogonal Coifman wavelets by recovering other \\\"missing\\\" members of the biorthogonal Coifman wavelet systems. We then propose and study the wavelet filters of the minimal synthesis norm. It is also demonstrated that an additional feature of the minimal norm will in general improve the compression performance of the codecs based on such wavelets.\",\"PeriodicalId\":236050,\"journal\":{\"name\":\"Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISSPA.2001.949787\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISSPA.2001.949787","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Wavelets of vanishing moments and minimal filter norms and the application to image compression
Wavelet systems of a maximum number of balanced vanishing moments are known to be extremely useful in a variety of applications including image and video compression. J. Tian and R.O. Wells Jr (see "Vanishing moments and biorthogonal wavelet systems", Mathematics in Signal Processing IV, Oxford University Press, 1997) recently created a family of such wavelet systems, called the biorthogonal Coifman wavelets, which proved valuable in both mathematics and applications. We first present an extension of Tian and Wells' family of biorthogonal Coifman wavelets by recovering other "missing" members of the biorthogonal Coifman wavelet systems. We then propose and study the wavelet filters of the minimal synthesis norm. It is also demonstrated that an additional feature of the minimal norm will in general improve the compression performance of the codecs based on such wavelets.
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