Prewhitening for Rank-Deficient Noise in Subspace Methods for Noise Reduction

Per Christian Hansen, Søren Holdt Jensen

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    Abstract

    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.
    Original languageEnglish
    JournalI E E E Transactions on Signal Processing
    Volume53
    Issue number10/1
    Pages (from-to)3718-3726
    ISSN1053-587X
    DOIs
    Publication statusPublished - 2005

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