Adaptive directional Haar tight framelets on bounded domains for digraph signal representations

2020/08/27 by Yuchen Xiao, Xiao, Yuchen, Xiaosheng Zhuang +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Advanced Data Compression Techniques #Fibroblast Growth Factor Research #Mathematical Analysis and Transform Methods #cs.LG #eess.SP #math.FA

paper · pdf · doi:10.48550/arxiv.2008.11966

arxiv created 2020/08/27 · arxiv updated 2020/08/28

Abstract

Based on hierarchical partitions, we provide the construction of Haar-type tight framelets on any compact set K⊆ 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.

Citations

• Laplacians and the Cheeger Inequality for Directed Graphs
• The Structure and Function of Complex Networks

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