Sampling and Reconstruction of Band-limited Graph Signals using Graph Syndromes

Abstract

The problem of sampling and reconstruction of band-limited graph signals is considered in this paper. A new sampling and reconstruction method based on the idea of error and erasure correction is proposed. We visualize the process of sampling as removal of nodes akin to introducing erasures, due to which the graph syndromes of a sampled signal gives rise to significant values, which otherwise would be minuscule for a band-limited signal. A reconstruction method by making use of these significant values in the graph syndromes is described and correspondingly the necessary and sufficient conditions for unique recovery and some key properties is provided. Additionally, this method allows for robust reconstruction i.e., reconstruction in the presence of few corrupted sampled nodes and a method based on weighted $\ell_{1}$ - norm is described. Simulation results are provided to demonstrate the efficiency of the method which shows better mean squared error performance compared to existing methods.