  In this paper, we consider Wiener filters to reconstruct deterministic and
(wide-band) stationary graph signals from their observations corrupted by
random noises, and we propose distributed algorithms to implement Wiener
filters and inverse filters on networks in which agents are equipped with a
data processing subsystem for limited data storage and computation power, and
with a one-hop communication subsystem for direct data exchange only with their
adjacent agents. The proposed distributed polynomial approximation algorithm is
an exponential convergent quasi-Newton method based on Jacobi polynomial
approximation and Chebyshev interpolation polynomial approximation to analytic
functions on a cube. Our numerical simulations show that Wiener filtering
procedure performs better on denoising (wide-band) stationary signals than the
Tikhonov regularization approach does, and that the proposed polynomial
approximation algorithms converge faster than the Chebyshev polynomial
approximation algorithm and gradient decent algorithm do in the implementation
of an inverse filtering procedure associated with a polynomial filter of
commutative graph shifts.
