Low-Distortion MMSE Speech Enhancement Estimator Based on Laplacian Prior

The most well-known conventional speech enhancement algorithms introduce unwanted artifact noise and speech distortion to the enhanced signal. Reducing the effects of such issues require more robust linear and non-linear estimators. This paper proposes new optimum linear and non-linear Laplacian distribution-based estimators. The proposed estimators are derived based on a minimum mean squared error (MMSE) sense to minimize the distortion in different conditions of the underlying speech. Thus, artifact noise is reduced without compromising the noise reduction process. The analytical solutions of the Laplacian distribution-based estimators, linear bilateral Laplacian gain estimator (LBLG), and non-linear bilateral Laplacian gain estimator (NBLG), are presented. The proposed estimators are implemented in three steps. First, the observation signal is decorrelated through a real transform domain to obtain its transform coefficients. Second, the proposed estimators are applied to estimate the clean speech signal from the noisy signal in the decorrelated domain. Finally, the inverse of the real transform is applied to obtain the original speech signal in the time domain. Two conditions in these estimators account for interference events between the speech signal and noise coefficients in the decorrelated domain. Moreover, a mathematical aspect of mean square error of LBLG is evaluated, which presents a significant improvement over other methods. Furthermore, a comprehensive description of the whole variations of the LBLG and NBLG gains characteristics is presented. A comparative evaluation is performed with effective quality metrics, segmental signal-to-noise ratio and perceptual evaluation of speech quality, to demonstrate the advantage and effectiveness of the proposed estimators. The performance of the proposed estimators outperformed other methods, which are the traditional MMSE approach, perceptually motivated Bayesian estimator, dual gain Wiener estimator, and dual MMSE estimator in terms of different objective measurements.