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Adaptive Directional Haar Tight Framelets on Bounded Domains for Digraph Signal Representations

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Abstract

Based on hierarchical partitions, we provide the construction of Haar-type tight framelets on any compact set \(K\subseteq \mathbb {R}^d\). In particular, on the unit block \([0,1]^d\), such tight framelets can be built to be with adaptivity and directionality. We show that the adaptive directional Haar tight framelet systems can be used for digraph signal representations. Some examples are provided to illustrate results in this paper.

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Acknowledgements

The authors thank the anonymous reviewers for their constructive comments and valuable suggestions that greatly help the improvement of the quality of the paper. The research and the work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11301419) and City University of Hong Kong (Project No. 7005497)

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  1. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong

    Yuchen Xiao & Xiaosheng Zhuang

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  1. Yuchen Xiao
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Xiao, Y., Zhuang, X. Adaptive Directional Haar Tight Framelets on Bounded Domains for Digraph Signal Representations. J Fourier Anal Appl 27, 7 (2021). https://doi.org/10.1007/s00041-021-09816-3

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