<p>Compared to traditional (scalar) framelets, multiframelets (or vector framelets) are more compatible with good properties and are more flexible to construct. For a multiframelet filter bank, its balancing property is crucial, as having a high balancing order means the associated discrete multiframelet transform is sparse. This paper provides a comprehensive characterization of balanced multiframelet filter banks. We will establish the necessary and sufficient conditions for a multiframelet filter bank to have the highest possible balancing order. Such a characterization is easy to verify and provides a clear guideline on constructing balanced multiframelets filter banks, yielding a straightforward construction algorithm. We will give some examples to illustrate our theory at the end of the paper.</p>

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Characterizing balanced dual multiframelet filter banks

  • Ran Lu

摘要

Compared to traditional (scalar) framelets, multiframelets (or vector framelets) are more compatible with good properties and are more flexible to construct. For a multiframelet filter bank, its balancing property is crucial, as having a high balancing order means the associated discrete multiframelet transform is sparse. This paper provides a comprehensive characterization of balanced multiframelet filter banks. We will establish the necessary and sufficient conditions for a multiframelet filter bank to have the highest possible balancing order. Such a characterization is easy to verify and provides a clear guideline on constructing balanced multiframelets filter banks, yielding a straightforward construction algorithm. We will give some examples to illustrate our theory at the end of the paper.