  In this paper, we consider nonsubsampled graph filter banks (NSGFBs) to
process data on a graph in a distributed manner. Given an analysis filter bank
with small bandwidth, we propose algebraic and optimization methods of
constructing synthesis filter banks such that the corresponding NSGFBs provide
a perfect signal reconstruction in the noiseless setting. Moreover, we prove
that the proposed NSGFBs can control the resonance effect in the presence of
bounded noise and they can limit the influence of shot noise primarily to a
small neighborhood of its location on the graph. For an NSGFB on a graph of
large size, a distributed implementation has a significant advantage, since
data processing and communication demands for the agent at each vertex depend
mainly on its neighboring topology. In this paper, we propose an iterative
distributed algorithm to implement the proposed NSGFBs. Based on NSGFBs, we
also develop a distributed denoising technique which is demonstrated to have
satisfactory performance on noise suppression.
