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 super-set 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.

We present a multichannel speech enhancement method based on MAP speech spectral magnitude estimation using a generalized gamma model of speech prior distribution, where the model parameters are adapted from actual noisy speech in a frame-by-frame manner. The utilization of a more general prior distribution with its online adaptive estimation is shown to be effective for speech spectral estimation in noisy environments. Furthermore, the multi-channel information in terms of cross-channel statistics are shown to be useful to better adapt the prior distribution parameters to the actual observation, resulting in better performance of speech enhancement algorithm. We tested the proposed algorithm in an in-car speech database and obtained significant improvements of the speech recognition performance, particularly under non-stationary noise conditions such as music, air-conditioner and open window.