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 any compact set $$K\subseteq \mathbb {R}^d$$ . In particular, unit block $$[0,1]^d$$ , such can be built to with adaptivity and directionality. We show that adaptive directional Haar framelet systems used for digraph signal representations. Some examples are provided illustrate results in this paper.