Subgraph-based Tight Frames on Graphs with Compact Supports and Vanishing Moments

In this work, we proposed a novel and general method to construct tight frames on graphs with compact supports based on a series of hierarchical partitions. Starting from our abstract construction that generalizes previous methods based on partition trees, we are able to flexibly incorporate subgraph Laplacians into our design of graph frames. Consequently, our general methods permit adjusting the (subgraph) vanishing moments of the framelets and extra properties, such as directionality, for efficiently representing graph signals with path-like supports. Several variants are explicitly defined and tested. Experimental results show our proposed graph frames perform superiorly in non-linear approximation tasks.