  Graph signals offer a very generic and natural representation for data that
lives on networks or irregular structures. The actual data structure is however
often unknown a priori but can sometimes be estimated from the knowledge of the
application domain. If this is not possible, the data structure has to be
inferred from the mere signal observations. This is exactly the problem that we
address in this paper, under the assumption that the graph signals can be
represented as a sparse linear combination of a few atoms of a structured graph
dictionary. The dictionary is constructed on polynomials of the graph
Laplacian, which can sparsely represent a general class of graph signals
composed of localized patterns on the graph. We formulate a graph learning
problem, whose solution provides an ideal fit between the signal observations
and the sparse graph signal model. As the problem is non-convex, we propose to
solve it by alternating between a signal sparse coding and a graph update step.
We provide experimental results that outline the good graph recovery
performance of our method, which generally compares favourably to other recent
network inference algorithms.
