On MMSE-Based Estimation of Amplitude and Complex Speech Spectral Coefficients Under Phase-Uncertainty

Among the most commonly used single-channel approaches for the enhancement of noise corrupted speech are Bayesian estimators of clean speech coefficients in the short-time Fourier transform domain. However, the vast majority of these approaches effectively only modifies the spectral amplitude and does not consider any information about the clean speech spectral phase. More recently, clean speech estimators that can utilize prior phase information have been proposed and shown to lead to improvements over the traditional, phase-blind approaches. In this work, we revisit phase-aware estimators of clean speech amplitudes and complex coefficients. To complete the existing set of estimators, we first derive a novel amplitude estimator given uncertain prior phase information. Second, we derive a closed-form solution for complex coefficients when the prior phase information is completely uncertain or not available. We put the novel estimators into the context of existing estimators and discuss their advantages and disadvantages.