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.

中文翻译：

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有界域上的自适应方向性Haar紧小框架用于有向图信号表示

基于分层分区，我们在任何紧凑集\（K \ subseteq \ mathbb {R} ^ d \）上提供Haar型紧框架。特别地，在单位块\ [[[0,1] ^ d \）上，可以构建这种紧密的框架，使其具有适应性和方向性。我们证明了自适应方向性Haar紧小框架系统可以用于有向图信号表示。提供了一些示例来说明本文的结果。