Speech enhancement using a joint map estimator with Gaussian mixture model for (non-)stationary noise

In many applications non-stationary Gaussian or stationary non Gaussian noises can be observed. In this paper we present a maximum a posteriori estimation jointly of spectral amplitude and phase (JMAP). It principally allows for arbitrary speech models (Gaussian, super-Gaussian, ...), while the noise DFT coefficients pdf is modeled as Gaussian mixture (GMM). Such a GMM covers both a non-Gaussian stationary noise process, but also a non-stationary process that changes between Gaussian noise modes of different variance with probability of the GMM weight. Accordingly, we provide results for these two types of noise, showing superiority over the Gaussian noise model JMAP estimator even in case of ideal noise power estimation.