Single-channel noise reduction via semi-orthogonal transformations and reduced-rank filtering

• A general framework is developed that combines semi-orthogonal transformation and reduced-rank filtering for noise reduction.
• Under this new framework, several optimal reduced-rank filters are derived, including the maximum SNR, the Wiener, the tradeoff, and the MVDR filters.
• Discussions are also provided on how to derive different semi-orthogonal transformations under four estimation criteria, including minimum correlation, minimum MSE, minimum distortion, and minimum residual noise.
• Simulations are performed and the results show the properties of the deduced optimal reduced-rank filters.

This paper investigates the problem of single-channel noise reduction in the time domain. The objective is to find a lower dimensional filter that can yield a noise reduction performance as close as possible to or even better than that obtained by the full-rank solution. This is achieved in three steps. First, we transform the observation signal vector sequence, through a semi-orthogonal matrix, into a sequence of transformed signal vectors with a reduced dimension. Second, a reduced-rank filter is applied to get an estimate of the clean speech in the transformed domain. Third, the estimate of the clean speech in the time domain is obtained by an inverse semi-orthogonal transformation. The focus of this paper is on the derivation of semi-orthogonal transformations under certain estimation criteria in the first step and the design of the reduced-rank optimal filters that can be used in the second step. We show how noise reduction using the principle of rank reduction can be cast as an optimal filtering problem, and how different semi-orthogonal transformations affect the noise reduction performance. Simulations are performed under various conditions to validate the deduced filters for noise reduction.