A Novel Scheme for Support Identification and Iterative Sampling of Bandlimited Graph Signals

We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction error. We propose an efficient iterative selection sampling approach and show that in the noiseless case the original signal is exactly recovered from the set of selected nodes. In the case of noisy measurements, a bound on the reconstruction error of the proposed algorithm is established. We further address the support identification of the bandlimited signal with unknown support and show that under a pragmatic sufficient condition, the proposed framework requires minimal number of samples to perfectly identify the support. The efficacy of the proposed methods are illustrated through numerical simulations on synthetic and real-world graphs

Accelerated Sampling of Bandlimited Graph Signals

We study the problem of sampling and reconstructing bandlimited graph signals where the objective is to select a subset of nodes of pre-specified cardinality that ensures interpolation of the original signal with the lowest possible reconstruction error. First, we consider a non-Bayesian scenario and propose an efficient iterative sampling procedure that in the noiseless case enables exact recovery of the original signal from the set of selected nodes. In the case of noisy measurements, a bound on the reconstruction error of the proposed algorithm is established. Then, we consider the Bayesian scenario where we formulate the sampling task as the problem of maximizing a monotone weak submodular function, and propose a randomized-greedy algorithm to find a sub-optimal subset. We derive a worst-case performance guarantee on the mean-square error achieved by the randomized-greedy algorithm for general non-stationary graph signals. The efficacy of the proposed methods is illustrated through extensive numerical simulations on synthetic and real-world graphs.Comment: arXiv admin note: text overlap with arXiv:1807.0718