  Graph signal processing (GSP) studies signals that live on irregular data
kernels described by graphs. One fundamental problem in GSP is sampling---from
which subset of graph nodes to collect samples in order to reconstruct a
bandlimited graph signal in high fidelity. In this paper, we seek a sampling
strategy that minimizes the mean square error (MSE) of the reconstructed
bandlimited graph signals assuming an independent and identically distributed
(iid) noise model---leading naturally to the A-optimal design criterion. To
avoid matrix inversion, we first prove that the inverse of the information
matrix in the A-optimal criterion is equivalent to a Neumann matrix series. We
then transform the truncated Neumann series based sampling problem into an
equivalent expression that replaces eigenvectors of the Laplacian operator with
a sub-matrix of an ideal low-pass graph filter. Finally, we approximate the
ideal filter using a Chebyshev matrix polynomial. We design a greedy algorithm
to iteratively minimize the simplified objective. For signal reconstruction, we
propose an accompanied signal reconstruction strategy that reuses the
approximated filter sub-matrix and is provably more robust than conventional
least square recovery. Simulation results show that our sampling strategy
outperforms two previous strategies in MSE performance at comparable
complexity.
