Higher order statistics-driven magnitude and phase spectrum estimation for speech enhancement

Higher order statistics (HOS), can be effectively employed for noise suppression, provided the noise follows a Gaussian distribution. Since most of the noises are distributed normally, HOS can be effectively used for speech enhancement in noisy environments. In the current work, HOS-based parametric modelling for magnitude spectrum estimation is proposed to improve the SNR under noisy conditions. To establish this, a non-Gaussian reduced ARMA model formulated using third order cumulant sequences (Giannakis, 1990) is used. Here, the AR and MA model orders, $p$ and $q$, are dynamically estimated by the well-established periodicity estimation technique under noisy conditions namely the Ramanujan Filter Bank (RFB) approach. The AR coefficients estimated from the reduced ARMA model are used to obtain the partially enhanced speech output, whose magnitude spectrum is then subjected to second-level enhancement using log MMSE with modified speech presence uncertainty (SPU) estimation technique. The refined magnitude spectrum, is combined with the phase spectrum extracted using proposed bicoherence-based phase compensation (BPC) technique, to estimate the enhanced speech output. The HOS-driven speech enhancement technique proposed in the current work is observed to be efficient for white, pink, babble and buccaneer noises. The objective measures, PESQ and STOI, indicate that the proposed method works well under all the noise conditions considered for evaluation.