Gamma Modeling of Speech Power and Its On-Line Estimation for Statistical Speech Enhancement

This study shows the effectiveness of using gamma distribution in the speech power domain as a more general prior distribution for the model-based speech enhancement approaches. This model is a superset of the conventional Gaussian model of the complex spectrum and provides more accurate prior modeling when the optimal parameters are estimated. We develop a method to adapt the modeled distribution parameters from each actual noisy speech in a frame-by-frame manner. Next, we derive and investigate the minimum mean square error (MMSE) and maximum a posterior probability (MAP) estimations in different domains of speech spectral magnitude, generalized power and its logarithm, using the proposed gamma modeling. Finally, a comparative evaluation of the MAP and MMSE filters is conducted. As the MMSE estimations tend to more complicated using more general prior distributions, the MAP estimations are given in closed-form extractions and therefore are suitable in the implementation. The adaptive estimation of the modeled distribution parameters provides more accurate prior modeling and this is the principal merit of the proposed method and the reason for the better performance. From the experiments, the MAP estimation is recommended due to its high efficiency and low complexity. Among the MAP based systems, the estimation in log-magnitude domain is shown to be the best for the speech recognition as the estimation in power domain is superior for the noise reduction. key words: speech enhancement, speech recognition, gamma modeling, fourth-order moment, MMSE, MAP, spectral magnitude, power, logspectral magnitude