Speech enhancement using MMSE estimation of amplitude and complex speech spectral coefficients under phase-uncertainty

Traditional speech enhancement algorithms are based on amplitude only processing, in which the amplitudes of speech are processed and phase is left unprocessed. Recently, Short Time Fourier Transform (STFT) based single channel speech enhancement algorithms are developed by considering prior knowledge of phase and its uncertainty. The uncertain knowledge of the phase is obtained from the phase reconstruction algorithms. The goal of this paper is twofold. One is deriving Joint Minimum Mean Square Error (MMSE) estimate of Complex speech coefficients given Uncertainty Phase (CUP) by assuming the speech coefficients as Nagakami, Gamma and noise distribution as Generalized Gamma distribution (GGD). Also estimators of type, Amplitudes given Uncertainty Phase (AUP), which uses uncertain phase only for amplitude estimation and not for phase improvement are derived. Also Novel Phase- blind estimators are developed using Nagakami PDF / Gamma as speech priors and Generalized Gamma as Noise Prior. Finally comparison of all estimators using uncertain prior phase information is discussed and how initial phase information affects the enhancement process is analyzed with novel estimators. The proposed CUP estimator outperforms the existing algorithms in terms of objective performance measures Segmental Signal to Noise Ratio (SSNR), Phase Signal to Noise Ratio (PSNR), Perceptual Evaluation of Speech Quality (PESQ), and Short Time Objective Intelligibility (STOI). Secondly, a combination of statistical based approach and Non-negative Matrix Factorization (NMF) based speech enhancement technique, in which bases are update on-line is discussed. The proposed estimator gain is used with NMF and analyzes its performance using PESQ measure.