Aggregation sampling of graph signals in the presence of noise

A scheme to sample bandlimited graph signals in the presence of noise is analyzed. Samples are aggregated at a single node by successive applications of the so-called graph-shift operator that encodes the local structure of the underlying graph. In contrast to the noiseless case, when noise is present the choice of the sampling node and the local sample-selection scheme plays a major role in determining the interpolation error. We provide optimal sampling schemes for particular noise models. We also analyze and provide identifiability conditions for the case where the frequency support of the bandlimited signal is unknown. Finally, simulations with synthetic and real-world graph signals are used to illustrate the behavior of aggregation sampling in noisy scenarios.