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 ${\mathbf{C}}_k$ 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.

在本文中，我们研究了语音信号的图形表示和图形语音增强技术。具体来说，我们首先提出一个新图$ķ$班次操作员 ${\mathbf{C}}_{ķ}$通过将语音信号的奇异特征向量用于语音图信号（SGS），将语音信号映射到图域，并构造一个新颖的图傅立叶基础。在此基础上，我们提出了一种基于最小均方误差（MMSE）准则的改进的图维纳滤波方法，以抑制嘈杂语音中的噪声干扰。数值仿真结果表明，与DSP中的传统方法和在GSP中应用图移位算符的现有图维纳滤波方法相比，该方法的性能在平均SSNR和平均PESQ得分方面均优于这些方法。此外，所提出的方法的计算复杂度比现有的图维纳滤波方法低得多，并且比DSP中的经典方法高一些。