A Learning Time-Graph Frequency Representation for Monaural Speech Enhancement

The Graph Fourier Transform (GFT) has recently demonstrated promising results in speech enhancement. However, existing GFT-based speech enhancement approaches often employ fixed graph topologies to build the graph Fourier basis, whose the representation lacks the adaptively and flexibility. In addition, they suffer from the numerical errors and instability introduced by matrix inversion in GFT based on both Singular Value Decomposition (GFT-SVD) and Eigen Vector Decomposition (GFT-EVD). Motivated by these limitations, this paper propose a simple yet effective learnable GFT-SVD framework for speech enhancement. Specifically, we leverage graph shift operators to construct a learnable graph topology and define a learnable graph Fourier basis by the singular value matrices using 1-D convolution (Conv-1D) neural layer. This eliminates the need for matrix inversion, thereby avoiding the associated numerical errors and stability problem. In contrast to complex-valued representation, our proposed learnable Fourier basis provides a real-valued time-graph representation, enabling better magnitude–phase alignment in speech enhancement. Comprehensive evaluations on the VCTK+DEMAND and DNS-2020 benchmarks demonstrate the consistent performance superiority of our learnable GFT-SVD over fixed STFT, GFT-EVD, and GFT-SVD within existing neural speech enhancement frameworks. Source code is available at:https://github.com/Wangfighting0015/GFT_project.