Optimal estimators for spectral restoration of noisy speech

Acoustic noise suppression is treated as a problem of finding the minimum mean square error estimate of the speech spectrum from a noisy version. This estimate equals the expected value of its conditional distribution given the noisy spectral value, the mean noise power and the mean speech power. It is shown that speech is not Gaussian. This results in an optimal estimate which is a non-linear function of the spectral magnitude. This function differs from the Wiener filter, especially at high instantaneous signal-to-noise ratios. Since both speech and Gaussian noise have a uniform phase distribution, the optimal estimator of the phase equals the noisy phase. The paper describes how the estimator can be calculated directly from noise-free speech. It describes how to find the optimal estimator for the complex spectrum, the magnitude, the squared magnitude, the log magnitude, and the root-magnitude spectra. Results for a speaker dependent connected digit speech recognition task with a base error rate of 1.6%, show that preprocessing the noisy unknown speech with a 10 dB signal-to-noise ratio reduces the error rate from 42% to 10%. If the template data are also preprocessed in the same way, the error rate reduces to 2.1%, thus recovering 99% of the recognition performance lost due to noise.