Parameter Estimation Procedures for Deep Multi-Frame MVDR Filtering for Single-Microphone Speech Enhancement

Parameter Estimation Procedures for Deep Multi-Frame MVDR Filtering for Single-Microphone Speech Enhancement

Marvin Tammen, Simon Doclo

Aiming at exploiting temporal correlations across consecutive time frames in the short-time Fourier transform (STFT) domain, multi-frame algorithms for single-microphone speech enhancement have been proposed, which apply a complex-valued filter to the noisy STFT coefficients. Typically, the multi-frame filter coefficients are either estimated directly using deep neural networks or a certain filter structure is imposed, e.g., the multi-frame minimum variance distortionless response (MFMVDR) filter structure. Recently, it was shown that integrating the fully differentiable MFMVDR filter into an end-to-end supervised learning framework employing temporal convolutional networks (TCNs) allows for a high estimation accuracy of the required parameters, i.e., the speech inter-frame correlation vector and the interference covariance matrix. In this paper, we investigate different covariance matrix structures, namely Hermitian positive-definite, Hermitian positive-definite Toeplitz, and rank-1. The main difference between the considered matrix structures lies in the number of parameters that need to be estimated by the TCNs and hence the computational complexity. When assuming a rank-1 matrix structure, we show that the MFMVDR filter can be written as a linear combination of the TCN outputs, significantly reducing computational complexity. In addition, we consider a covariance matrix estimation procedure based on recursive smoothing, where the smoothing factors are estimated using TCNs. Experimental results on the deep noise suppression challenge 1 and 2 datasets show that the estimation procedure using the Hermitian positive-definite matrix structure yields the best performance, closely followed by the rank-1 matrix structure at a much lower complexity. Furthermore, it is shown for the best-performing MFMVDR filters that imposing the MFMVDR filter structure instead of directly estimating the multi-frame filter coefficients is beneficial in terms of speech enhancement performance.

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(Changed: 28 Nov 2022)