Optimal rectangular filtering matrix for noise reduction in the time domain

In this paper, we study the noise reduction problem in the time domain and present a frame-based method to decompose the clean speech vector into two orthogonal components: one correlated and the other uncorrelated with the current desired speech vector to be estimated. In comparison with the sample-based decomposition developed in the previous research that uses only forward prediction, this new decomposition exploits both the forward prediction and interpolation. Based on this new decomposition, we formulate different optimization cost functions and address the issue of how to design Wiener and minimum variance distortionless response (MVDR) filtering matrices by optimizing these new cost functions. We also discuss the relationship between the Wiener and MVDR filtering matrices and show that the MVDR filtering matrix can achieve noise reduction without adding speech distortion; but it reduces less noise than the Wiener filtering matrix. Compared with the sample-based algorithms developed in the previous study, the proposed frame-based algorithms can achieve better noise reduction performance. Furthermore, they are computationally more efficient, and therefore, more suitable for practical implementation.