A minimum variance partially distortionless response filter for single-channel noise reduction

This paper deals with the problem of single-channel noise reduction. Thanks to the eigenvalue decomposition, we arrange the eigenvalues of the speech correlation matrix in such a way that all the spectral mode signal-to-noise ratios (SNRs) of the noisy speech are ordered in a descending manner. By maintaining no speech distortion in the spectral modes with high input SNRs while allowing some degree of speech distortion in the modes with low input SNRs, we develop a minimum variance partially distortionless response (MVPDR) filter. We first formulate the problem and derive this filter within the general filtering framework. Then, the MVPDR filter is applied to the single-channel noise reduction problem in both the time and time-frequency domains. In comparison with the minimum variance distortionless response (MVDR) filter based on the subspace decomposition, the developed MVPDR filter can provide much more freedom for controlling the compromise between noise reduction and speech distortion to achieve higher speech quality. Simulations are conducted and preliminary results justify the advantages of the deduced MVPDR filter.