Comparison of complex-DFT estimators with and without the independence assumption of real and imaginary parts

MMSE estimators for DFT-domain based single-microphone speech enhancement can broadly be classified in those that estimate the complex-DFT coefficients and those that estimate the DFT magnitudes. Existing complex-DFT MMSE estimators have generally been derived under assumptions that are in conflict with measured histograms and that are inconsistent with the assumptions made to derive DFT magnitude estimators. Recently it has been shown that these inconsistencies can be eliminated, i.e., no independency has to be assumed between real and imaginary parts of DFT coefficients if the phase of DFT coefficients is assumed uniformly distributed. In this paper we discuss the assumptions that underlie the different complex-DFT estimators and show that the uniform phase assumption matches actual speech data. Furthermore, we show experimentally that the estimators without the independence assumption lead to a lower mean-square error.