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We introduce graph wedgelets - a tool for data compression on graphs based onthe representation of signals by piecewise constant functions on adaptivelygenerated binary graph partitionings. The adaptivity of the partitionings, akey ingredient to obtain sparse representations of a graph signal, is realizedin terms of recursive wedge splits adapted to the signal. For this, we transferadaptive partitioning and compression techniques known for 2D images to generalgraph structures and develop discrete variants of continuous wedgelets andbinary space partitionings. We prove that continuous results on best m-termapproximation with geometric wavelets can be transferred to the discrete graphsetting and show that our wedgelet representation of graph signals can beencoded and implemented in a simple way. Finally, we illustrate that thisgraph-based method can be applied for the compression of images as well.

Graph Wedgelets: Adaptive Data Compression on Graphs based on Binary Wedge Partitioning Trees and Geometric Wavelets