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Optimal single-channel noise reduction filtering matrices from the pearson correlation coefficient perspective

This paper studies the problem of single-channel noise reduction in the time domain, where an estimate of a vector of the desired clean speech is achieved by filtering a frame of the noisy signal with a rectangular filtering matrix. The core issue with this problem formulation is then the estimation of the optimal filtering matrix. The squared Pearson correlation coefficient (SPCC) is used. We show that different optimal filtering matrices can be derived by maximizing or minimizing the SPCCs between different signals. For example, maximizing the SPCC between the enhanced signal and the filtered speech gives the reduced-rankWiener and minimum distortion (MD) filtering matrices while minimizing the SPCC gives the minimum noise (MN) and another reduced-rank Wiener filtering matrices. Simulation results are presented to illustrate the properties of these filtering matrices.