Local measurement and reconstruction for noisy bandlimited graph signals

Signals and information related to networks can be modeled and processed as graph signals. It has been shown that if a graph signal is smooth enough to satisfy certain conditions, it can be uniquely determined by its decimation on a subset of vertices. However, instead of the decimation, sometimes local combinations of signals on different sets of vertices are obtained in potential applications such as sensor networks with clustering structures. In this work, a generalized sampling scheme is proposed based on local measurement, which is a linear combination of signals associated with local vertices. It is proved that bandlimited graph signals can be perfectly reconstructed from the local measurements through a proposed iterative local measurement reconstruction (ILMR) algorithm. Some theoretical results related to ILMR including its convergence and denoising performance are given. Then the optimal partition of local sets and local weights are studied to minimize the error bound. It is shown that in noisy scenarios the proposed local measurement scheme is more robust than the traditional decimation scheme.