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

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

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...

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Veröffentlicht in:The Journal of fourier analysis and applications 2021-04, Vol.27 (2), Article 7
Hauptverfasser: Xiao, Yuchen, Zhuang, Xiaosheng
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Adaptive systems
Analysis
Approximations and Expansions
Computational linguistics
Fourier Analysis
Graph theory
Harmonic Analysis on Combinatorial Graphs
Language processing
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Natural language interfaces
Partial Differential Equations
Representations
Signal,Image and Speech Processing
Social networks
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Beschreibung
Zusammenfassung: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.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-021-09816-3