Pascal Frossard , associate professor at Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland
Abstract: The representation of signals residing on weighted graphs ideally has to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model graph signals as combinations of overlapping local patterns. We impose the constraint that each dictionary is a concatenation of subdictionaries, with each subdictionary being a polynomial of the graph Laplacian matrix, representing a single pattern translated to different areas of the graph. Illustrative applications of such dictionaries will be discussed in distributed signal processing and visual data representation. We will finally discuss how the graph signal representation framework can be used in the challenging problem of learning graph and geometry from data, and show a few illustrative results in different datasets.