Speech signal processing on graphs: The graph frequency analysis and an improved graph Wiener filtering method

In the paper, we investigate a graph representation of speech signals and graph speech enhancement technology. Specifically, we first propose a new graph k-shift operator Ck to map speech signals into the graph domain and construct a novel graph Fourier basis by using its singular eigenvectors for speech graph signals (SGSs). On this basis, we propose an improved graph Wiener filtering method based on the minimum mean square error (MMSE) criterion to suppress the noise interference in noisy speech. Comparing with the traditional methods in DSP and the existed graph Wiener filtering methods by applying graph shift operators in GSP, our numerical simulation results show that the performance of the proposed method outperforms that of these methods in terms of both average SSNR and mean PESQ score. Moreover, the computational complexity of the proposed method is much lower than that of the existed graph Wiener filtering methods and a little higher than that of classical methods in DSP.