Bayesian Estimation of Clean Speech Spectral Coefficients Given a Priori Knowledge of the Phase

While most short-time discrete Fourier transform-based single-channel speech enhancement algorithms only modify the noisy spectral amplitude, in recent years the interest in phase processing has increased in the field. The goal of this paper is twofold. First, we derive Bayesian probability density functions and estimators for the clean speech phase when different amounts of prior knowledge about the speech and noise amplitudes is given. Second, we derive a joint Bayesian estimator of the clean speech amplitudes and phases, when uncertain a priori knowledge on the phase is available. Instrumental measures predict that by incorporating uncertain prior information of the phase, the quality and intelligibility of processed speech can be improved both over traditional phase insensitive approaches, and approaches that treat prior information on the phase as deterministic.