A reconstruction method for graph signals based on the power spectral density estimation

Abstract

Graph signal reconstruction is a classic problem of graph signal processing. The ultimate goal of signal reconstruction is to obtain an estimate as close as possible to the original signals. Most of existing reconstruction models are based on assumption of signal smoothness. This paper proposes a new reconstruction model based on signal power spectral density estimation. The basic idea is to suppress those graph frequency components with low power spectral density when reconstructing a signal, while preserving those graph frequency contents with high power spectral density. Therefore, the reconstructed signals can well maintain the frequency structures of the original signals. Under the stationarity assumption of stochastic graph signals, we further propose a method to estimate the power spectral density directly from the sampled signals. Experimental results show that the proposed power spectral density estimation algorithm works well even when the proportion of labeled vertices is extremely low, and is robust to the PSD of signals itself and the various structures of graphs. Compared with traditional models based on smoothness assumption, the proposed reconstruction model can significantly improve the reconstruction performance.