Reconstruction of bandlimited graph signals from random local sampling

Sampling and reconstruction on the spatially distributed networks is an innovative topic in graph signal processing. Recently, it has been shown that k-bandlimited graph signals can be reconstructed from a random collection of physically constrained sampled data. In this paper, we first study the random sampling scheme of k-bandlimited signals from a general local measurement, and then an iterative reconstruction algorithm based on frame theory is proposed with exponential convergence. It can yield a distributed implementation at a vertex level, which enables the devices that are limited by storage and computing power to recover signals more effectively. Numerical experiments on synthetic and real-world data are performed to validate the effectiveness of the proposed approach.