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- W4319866331 abstract "We introduce graph wedgelets - a tool for data compression on graphs based on the representation of signals by piecewise constant functions on adaptively generated binary graph partitionings. The adaptivity of the partitionings, a key ingredient to obtain sparse representations of a graph signal, is realized in terms of recursive wedge splits adapted to the signal. For this, we transfer adaptive partitioning and compression techniques known for 2D images to general graph structures and develop discrete variants of continuous wedgelets and binary space partitionings. We prove that continuous results on best <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$m$</tex-math></inline-formula> -term approximation with geometric wavelets can be transferred to the discrete graph setting and show that our wedgelet representation of graph signals can be encoded and implemented in a simple way. Finally, we illustrate that this graph-based method can be applied for the compression of images as well." @default.
- W4319866331 created "2023-02-11" @default.
- W4319866331 creator A5036671307 @default.
- W4319866331 date "2023-01-01" @default.
- W4319866331 modified "2023-09-26" @default.
- W4319866331 title "Graph Wedgelets: Adaptive Data Compression on Graphs Based on Binary Wedge Partitioning Trees and Geometric Wavelets" @default.
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- W4319866331 doi "https://doi.org/10.1109/tsipn.2023.3240899" @default.
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