Spectral Domain Speech Enhancement Using HMM State-Dependent Super-Gaussian Priors

The derivation of MMSE estimators for the DFT coefficients of speech signals, given an observed noisy signal and super-Gaussian prior distributions, has received a lot of interest recently. In this letter, we look at the distribution of the periodogram coefficients of different phonemes, and show that they have a gamma distribution with shape parameters less than one. This verifies that the DFT coefficients for not only the whole speech signal but also for individual phonemes have super-Gaussian distributions. We develop a spectral domain speech enhancement algorithm, and derive hidden Markov model (HMM) based MMSE estimators for speech periodogram coefficients under this gamma assumption in both a high uniform resolution and a reduced-resolution Mel domain. The simulations show that the performance is improved using a gamma distribution compared to the exponential case. Moreover, we show that, even though beneficial in some aspects, the Mel-domain processing does not lead to better results than the algorithms in the high-resolution domain.