  We propose a generalized sampling framework for stochastic graph signals.
Stochastic graph signals are characterized by graph wide sense stationarity
(GWSS) which is an extension of wide sense stationarity (WSS) for standard
time-domain signals. In this paper, graph signals are assumed to satisfy the
GWSS conditions and we study their sampling as well as recovery procedures. In
generalized sampling, a correction filter is inserted between sampling and
reconstruction operators to compensate for non-ideal measurements. We propose a
design method for the correction filters to reduce the mean-squared error (MSE)
between original and reconstructed graph signals. We derive the correction
filters for two cases: The reconstruction filter is arbitrarily chosen or
predefined. The proposed framework allows for arbitrary sampling methods, i.e.,
sampling in the vertex or graph frequency domain. We also show that the graph
spectral response of the resulting correction filter parallels that for
generalized sampling for WSS signals if sampling is performed in the graph
frequency domain. Furthermore, we reveal the theoretical connection between the
proposed and existing correction filters. The effectiveness of our approach is
validated via experiments by comparing its MSE with existing approaches.
