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Graph sampling addresses the problem of selecting a node subset in a graph tocollect samples, so that a K-bandlimited signal can be reconstructed in highfidelity. Assuming an independent and identically distributed (i.i.d.) noisemodel, minimizing the expected mean square error (MMSE) leads to the knownA-optimality criterion for graph sampling, which is expensive to compute anddifficult to optimize. In this paper, we propose an augmented objective basedon Neumann series that well approximates the original criterion and is amenableto greedy optimization. Specifically, we show that a shifted A-optimalcriterion can be equivalently written as a function of an ideal low-pass (LP)graph filter, which in turn can be approximated efficiently via fast graphFourier transform (FGFT). Minimizing the new objective, we select nodesgreedily without large matrix inversions using a matrix inverse lemma. Further,for the dynamic network case where node availability varies across time, wepropose an extended sampling strategy that replaces offline samples one-by-onein the selected set. For signal reconstruction, we propose an accompaniedbiased signal recovery strategy that reuses the approximated filter fromsampling. Experiments show that our reconstruction is more robust to largenoise than the least square (LS) solution, and our sampling strategy faroutperforms several existing schemes.

Low-complexity Graph Sampling with Noise and Signal Reconstruction via Neumann Series