Signal subspace approach for narrowband noise reduction in speech

A signal subspace method is proposed for speech enhancement in the presence of narrowband noise. A fundamental assumption in subspace methods for noise reduction is that the noise covariance matrix is positive definite. However, this is not always the case, especially when the noise has narrowband characteristics. Based on the eigenvalue decomposition of the rank deficient noise covariance matrix, it is shown how to formulate the enhancement algorithm by decomposing the vector space of noisy signal into a signal-plus-noise subspace and a noise-free subspace. The proposed subspace partition is different from the conventional subspace approaches in that the noise reduction algorithm is implemented using the whitening approach exclusively in the signal-plus-noise subspace. The enhancement is performed by estimating the clean speech from the signal-plus-noise subspace and adding the components in the noise-free subspace. An explicit form of the estimator is presented, and examples are illustrated to validate the effectiveness of the proposed method.