Accounting for the uncertainty of speech estimates in the complex domain for minimum mean square error speech enhancement

Uncertainty decoding and uncertainty propagation, or error propagation, techniques have emerged as a powerful tool to increase the accuracy of automatic speech recognition systems by employing an uncertain, or probabilistic, description of the speech features rather than the usual point estimate. In this paper we analyze the uncertainty generated in the complex Fourier domain when performing speech enhancement with the Wiener or Ephraim-Malah filters. We derive closed form solutions for the computation of the error of estimation and show that it provides a better insight into the origin of estimation uncertainty. We also show how the combination of such an error estimate with uncertainty propagation and uncertainty decoding or modified imputation yields superior recognition robustness when compared to conventional MMSE estimators with little increase in the computational cost.