An MMSE graph spectral magnitude estimator for speech signals residing on an undirected multiple graph

The paper uses the K -graphs learning method to construct weighted, connected, undirected multiple graphs, aiming to reveal intrinsic relationships of speech samples in the inter-frame and intra-frame. To benefit from the learned multiple graphs’ property and enhance interpretability, we study the spectral property of speech samples in the joint vertex-frequency domain by using the new graph weight matrix. Moreover, we propose the representation of minimum mean-square error (MMSE) graph spectral magnitude estimator for speech signals residing on undirected multiple graphs. We use the MMSE graph spectral magnitude estimator to improve speech enhancement performance. The numerical simulation results show that the proposed method outperforms the existing methods in graph signal processing (GSP) and the baseline methods for speech enhancement in discrete signal processing (DSP) in terms of PESQ, LLR, output SNR, and STOI results. These results also demonstrate the validity of the learned multiple graphs.