A Laplacian-based MMSE estimator for speech enhancement

This paper focuses on optimal estimators of the magnitude spectrum for speech enhancement. We present an analytical solution for estimating in the MMSE sense the magnitude spectrum when the clean speech DFT coefficients are modeled by a Laplacian distribution and the noise DFT coefficients are modeled by a Gaussian distribution. Furthermore, we derive the MMSE estimator under speech presence uncertainty and a Laplacian statistical model. Results indicated that the Laplacian-based MMSE estimator yielded less residual noise in the enhanced speech than the traditional Gaussian-based MMSE estimator. Overall, the present study demonstrates that the assumed distribution of the DFT coefficients can have a significant effect on the quality of the enhanced speech.