Ricerc@Sapienza

In the last years, several new tools have been devised to analyze signals defined over the vertices of a graph, i.e., over a discrete domain whose structure is described by pairwise relations. In this paper, we expand these tools to the analysis of signals defined on simplicial complexes, whose domain has a structure specified by various multi-way relations. Within this framework, we show how to filter signals and how to reconstruct edge and vertex signals from a subset of observations.

The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e. a set of points along with a set of neighborhood relations. This setup does not require the definition of a metric and then it is especially useful to deal with signals defined over non-metric spaces. We focus on signals defined over simplicial complexes. Graph Signal Processing (GSP) represents a special case of Topological Signal Processing (TSP), referring to the situation where the signals are associated only with the vertices of a graph.