Franziska Göbel (Universität Potsdam)
In this talk I will present a multiscale approach to construct a data-adapted basis-like (Parseval frame) set of functions F which allows for a decomposition of every square-integrable function defined on the vertices of a finite undirected weighted graph. We have a look at some properties of F and at its application in the denoising setup which is based on the property of being a Parseval frame. Related to the property of spatial localization we furthermore show that the considered random neighborhood graphs satisfy with high probability a doubling volume condition as well as a local Poincaré inequality under some assumptions on the underlying space and the sampling.
