Single-channel noise reduction using optimal rectangular filtering matrices

This paper studies the problem of single-channel noise reduction in the time domain and presents a block-based approach where a vector of the desired speech signal is recovered by filtering a frame of the noisy signal with a rectangular filtering matrix. With this formulation, the noise reduction problem becomes one of estimating an optimal filtering matrix. To achieve such estimation, a method is introduced to decompose a frame of the clean speech signal into two orthogonal components: One correlated and the other uncorrelated with the current desired speech vector to be estimated. Different optimization cost functions are then formulated from which non-causal optimal filtering matrices are derived. The relationships among these optimal filtering matrices are discussed. In comparison with the classical sample-based technique that uses only forward prediction, the block-based method presented in this paper exploits both the forward and backward prediction as well as the temporal interpolation and, therefore, can improve the noise reduction performance by fully taking advantage of the speech property of self correlation. There is also a side advantage of this block-based method as compared to the sample-based technique, i.e., it is computationally more efficient and, as a result, more suitable for practical implementation.