  In this paper, we incorporate a graph filter deconvolution step into the
classical geometric convolutional neural network pipeline. More precisely,
under the assumption that the graph domain plays a role in the generation of
the observed graph signals, we pre-process every signal by passing it through a
sparse deconvolution operation governed by a pre-specified filter bank. This
deconvolution operation is formulated as a group-sparse recovery problem, and
convex relaxations that can be solved efficiently are put forth. The
deconvolved signals are then fed into the geometric convolutional neural
network, yielding better classification performance than their unprocessed
counterparts. Numerical experiments showcase the effectiveness of the
deconvolution step on classification tasks on both synthetic and real-world
settings.
