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 wedge partitionings of a graph. For this, we transfer 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 $m$-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.
翻译：我们引入了图形 Wedgelets -- -- 图形数据压缩工具, 一种基于根据根据适应性生成的二进制 Wedge 分区图中信号的笔记式常数表示信号的图形数据压缩工具。 为此, 我们将2D 图像已知的分区和压缩技术传输到一般图形结构, 并开发连续 Wedgelets 和二进制空间分区图的离散变体。 我们证明, 以几何波列的最佳美元- 定期近似值的连续结果可以传输到离散的图表设置中, 并显示我们的图形信号 Wedgelet 表示方式可以简单编码和实施。 最后, 我们说明, 这个基于图形的方法也可以用于图像压缩 。
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