Biorthogonal Multiwavelets with Sampling Property and Application in Image Compression

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• 作者：Baobin Li ; Lizhong Peng
• 关键词：Multiwavelet ; Biorthogonal multiwavelet ; Analysis ; ready multiwavelet ; Transferring armlet order ; 42C40a ; 65T60 ; 15A23 ; 94A08
• 刊名：Circuits, Systems, and Signal Processing
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：35
• 期：3
• 页码：933-951
• 全文大小：1,326 KB
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• 作者单位：Baobin Li (1)
  Lizhong Peng (2)
  
  1. School of Computer and Control, University of Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China
  2. School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China
  
• 刊物类别：Engineering
• 刊物主题：Electronic and Computer Engineering
  
• 出版者：Birkh盲user Boston
• ISSN：1531-5878

文摘

This paper discusses biorthogonal multiwavelets with sampling property. In such systems, vector-valued refinable functions act as the sinc function in the Shannon sampling theorem, and their corresponding matrix-valued masks possess a special structure. In particular, for the multiplicity \(r=2\), a biorthogonal multifilter bank can be reduced to two scalar-valued filters. Moreover, if the vector-valued scaling functions are interpolating, three different concepts: balancing order, approximation order and analysis-ready order, will be shown to be equivalent. Based on this result, we introduce the transferring armlet order for constructing biorthogonal balanced multiwavelets with sampling property. Also, some balanced biorthogonal multiwavelets will be obtained. Finally, application of biorthogonal interpolating multiwavelets in image compression is discussed. Experiments show that for the same length, the biorthogonal multifilter bank is superior to the orthogonal case. Moreover, certain biorthogonal interpolating multiwavelets are also better than the classical Daubechies wavelets. Keywords Multiwavelet Biorthogonal multiwavelet Analysis-ready multiwavelet Transferring armlet order