Journal article
Prewhitening for Rank-Deficient Noise in Subspace Methods for 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 prewhitening step to be defined. However, there are important cases where this requirement is not fulfilled, e.g., when the noise has narrow-band characteristics, or in the case of tonal noise.
We extend the concept of prewhitening 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.
Finally we apply our algorithm to a problem involving a speech signal contaminated by narrow-band noise.
| Language: | English |
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| Publisher: | IEEE |
| Year: | 2005 |
| Pages: | 3718-3726 |
| ISSN: | 19410476 and 1053587x |
| Types: | Journal article |
| DOI: | 10.1109/TSP.2005.855110 |
| ORCIDs: | Hansen, Per Christian |
Covariance matrix Informatics Mathematics Matrix decomposition Narrowband Noise reduction Signal processing Signal processing algorithms Singular value decomposition Speech enhancement ULV decomposition covariance matrices covariance matrix narrowband noise noise reduction prewhitening noise quotient ULV decomposition rank deficient noise rank-reduction algorithm signal processing singular value decomposition speech enhancement speech signal subspace methods
