Optimal speech estimator considering room response as well as additive noise: Different approaches in low and high frequency range

This paper proposes minimum mean squared error (MMSE) speech signal estimation in a reverberant space using different optimal estimators in the low and high frequency ranges. At low frequencies, an MMSE spectral amplitude estimator divided by the spectral amplitude of a representative impulse response produces optimal performance. In the high frequency range, the MMSE estimator is computed based on its sufficient statistic: the maximum likelihood (ML) estimate. Inference is factored using a two-step algorithm: the maximum likelihood value of the source spectrum is first estimated using expectation-maximization (EM) under the assumption of the hidden room response with complex Gaussian pdf, then the MMSE source spectral estimate is computed.