  In this paper, we investigate the application of graph signal processing
(GSP) theory in speech enhancement. We first propose a set of shift operators
to construct graph speech signals, and then analyze their spectrum in the graph
Fourier domain. By leveraging the differences between the spectrum of graph
speech and graph noise signals, we further propose the graph spectral
subtraction (GSS) method to suppress the noise interference in noisy speech.
Moreover, based on GSS, we propose the iterative graph spectral subtraction
(IGSS) method to further improve the speech enhancement performance. Our
experimental results show that the proposed operators are suitable for graph
speech signals, and the proposed methods outperform the traditional basic
spectral subtraction (BSS) method and iterative basic spectral subtraction
(IBSS) method in terms of both signal-to-noise ratios (SNR) and mean Perceptual
Evaluation of Speech Quality (PESQ).
