Subspace-based Noise Reduction

A fundamental issue in connection with subspace methods for noise reduction is that the covariance matrix for the noise is required to have full rank, in order for the pre-whitening step to be defined. However, there are important cases where this requirement is not fulfilled, typically when the noise has narrow-band characteristics, including the case of tonal noise. We extend the concept of pre-whitening to include the case when the noise covariance matrix is rank deficient, using a weighted pseudoinverse and the quotient SVD, and we show how to formulate a general rank-reduction algorithm that works also for rank deficient noise. We also demonstrate how to formulate this algorithm by means of a quotient ULV decomposition, which allows for faster computation and updating. (Søren Holdt Jensen, Per Christian Hansen (Technical University of Denmark))