A Novel Risk-Estimation-Theoretic Framework for Speech Enhancement in Nonstationary and Non-Gaussian Noise Conditions

Abstract

We address the problem of suppressing background noise from noisy speech within a risk estimation framework, where the clean signal is estimated from the noisy observations by minimizing an unbiased estimate of a chosen risk function. For Gaussian noise, such a risk estimate was derived by Stein, which eventually went on to be called Stein's unbiased risk estimate (SURE). Stein's formalism is restricted to Gaussian noise and exclusive risk estimators have been developed for each noise type. On the other hand, we consider linear denoising functions and derive an unbiased risk estimate without making any assumption about the noise distribution. The proposed unbiased estimate depends only on the second-order statistics of noise and makes the proposed framework applicable to many practical denoising problems where the noise distribution is not known a priori, but one has access only to the samples of noise. We demonstrate the usefulness of the proposed methodology for speech enhancement using subband shrinkage, where the shrinkage parameters are obtained by minimizing the newly developed risk estimator. The proposed methodology is also applicable to nonstationary noise conditions. We show that the proposed denoising algorithm outperforms the state-of-the art algorithms in terms of standard speech-quality evaluation metrics.