Estimation of Network Processes via Blind Graph Multi-filter Identification

We study the problem of jointly estimating several network processes that are driven by the same input, recasting it as one of blind identification of a bank of graph filters. More precisely, we consider the observation of several graph signals – i.e., signals defined on the nodes of a graph – and we model each of these signals as the output of a different network process (represented by a graph filter) defined on a common known graph and driven by a common unknown input. Our goal is to recover the specifications of every network process by only observing the outputs. Since every process shares the same input, the estimation problems are coupled, and a joint inference method is proposed. We study two different scenarios, one where the orders of the filters are known, and one where they are not. For the former case we propose a least-squares approach and provide conditions for recovery. For the latter case, we put forth a sparse recovery algorithm with theoretical guarantees. Finally, we illustrate the methods here proposed via numerical experiments.