A Block-Based Linear MMSE Noise Reduction with a High Temporal Resolution Modeling of the Speech Excitation

A comprehensive linear minimum mean squared error (LMMSE) approach for parametric speech enhancement is developed. The proposed algorithms aim at joint LMMSE estimation of signal power spectra and phase spectra, as well as exploitation of correlation between spectral components. The major cause of this interfrequency correlation is shown to be the prominent temporal power localization in the excitation of voiced speech. LMMSE estimators in time domain and frequency domain are first formulated. To obtain the joint estimator, we model the spectral signal covariance matrix as a full covariance matrix instead of a diagonal covariance matrix as is the case in the Wiener filter derived under the quasi-stationarity assumption. To accomplish this, we decompose the signal covariance matrix into a synthesis filter matrix and an excitation matrix. The synthesis filter matrix is built from estimates of the all-pole model coefficients, and the excitation matrix is built from estimates of the instantaneous power of the excitation sequence. A decision-directed power spectral subtraction method and a modified multipulse linear predictive coding (MPLPC) method are used in these estimations, respectively. The spectral domain formulation of the LMMSE estimator reveals important insight in interfrequency correlations. This is exploited to significantly reduce computational complexity of the estimator. For resource-limited applications such as hearing aids, the performance-to-complexity trade-off can be conveniently adjusted by tuning the number of spectral components to be included in the estimate of each component. Experiments show that the proposed algorithm is able to reduce more noise than a number of other approaches selected from the state of the art. The proposed algorithm improves the segmental SNR of the noisy signal by 13 dB for the white noise case with an input SNR of 0 dB.