An unbiased risk estimator for Gaussian mixture noise distributions — Application to speech denoising

Abstract

We develop an unbiased estimate of mean-squared error (MSE), where the observations are assumed to be drawn from a Gaussian mixture (GM) distribution. Stein's unbiased risk estimate (SURE) is an unbiased estimate of the MSE, and was originally proposed for independent and identically distributed (i.i.d.) multivariate Gaussian observations. Subsequently, it was extended to the exponential family of distributions. In this paper, we extend the idea of SURE to observations drawn from a Gaussian mixture distribution (GMD). Since Gaussian mixture models (GMM) can model any given distribution sufficiently accurately, this generalized framework allows us to apply the SURE technique to the observations drawn from an arbitrary distribution. As an application, we consider the problem of denoising speech corrupted by a GM distributed noise. It is observed that the denoising performance of the algorithm developed using SURE based on GMD is superior in terms of the signal-to-noise ratio (SNR) and average segmental SNR (ASSNR), compared with that obtained using SURE based on the single Gaussian assumption.