1 research outputs found
Blind Identification of Invertible Graph Filters with Multiple Sparse Inputs
This paper deals with problem of blind identification of a graph filter and
its sparse input signal, thus broadening the scope of classical blind
deconvolution of temporal and spatial signals to irregular graph domains. While
the observations are bilinear functions of the unknowns, a mild requirement on
invertibility of the filter enables an efficient convex formulation, without
relying on matrix lifting that can hinder applicability to large graphs. On top
of scaling, it is argued that (non-cyclic) permutation ambiguities may arise
with some particular graphs. Deterministic sufficient conditions under which
the proposed convex relaxation can exactly recover the unknowns are stated,
along with those guaranteeing identifiability under the Bernoulli-Gaussian
model for the inputs. Numerical tests with synthetic and real-world networks
illustrate the merits of the proposed algorithm, as well as the benefits of
leveraging multiple signals to aid the (blind) localization of sources of
diffusion