Blind Demixing of Diffused Graph Signals

TL;DR

This paper introduces a method for blind demixing of diffused graph signals, jointly identifying graph filters and separating sparse inputs, with theoretical guarantees and empirical validation on synthetic and real data.

Contribution

It extends blind source separation to graph signals by jointly estimating graph filters and sparse inputs, providing theoretical conditions for successful recovery.

Findings

Theoretical conditions for demixing feasibility with multiple graphs.

Probabilistic bounds on successful signal recovery.

Empirical validation on synthetic and real-world graphs.

Abstract

Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the graph. Widely-used approaches assume that the observed signals can be viewed as outputs of graph filters (i.e., polynomials of a matrix representation of the graph) whose inputs have a particular structure. Diffused graph signals, which correspond to an originally sparse (node-localized) signal percolated through the graph via filtering, fall into this class. In that context, this paper deals with the problem of jointly identifying graph filters and separating their (sparse) input signals from a mixture of diffused graph signals, thus generalizing to the graph signal processing framework the classical blind demixing (blind source separation) of temporal and spatial signals. We first consider the scenario where the supporting graphs are different across the signals, providing a theorem for demixing feasibility along with probabilistic bounds on successful recovery. Additionally, an analysis of the degenerate problem of demixing with a single graph is also presented. Numerical experiments with synthetic and real-world graphs empirically illustrating the main theoretical findings close the paper.