MMSE estimation of magnitude-squared DFT coefficients with superGaussian priors

We present two minimum mean square error (MMSE) frequency domain estimators of the squared magnitude of a clean speech signal that is degraded by additive noise. These estimators are derived under the assumption that the DFT (discrete Fourier transform) coefficients of the clean speech are best modelled by the Gamma probability distribution function (PDF) instead of the common Gaussian PDF. The statistics of the perturbing noise is the Gaussian PDF in one case and the Laplacian PDF in the other. The estimators are used as noise reduction filters in the experimental evaluation. We give a comparison with a previously derived estimator which uses the Gaussian PDF as the PDF for speech and noise coefficients.

1. INTRODUCTION

Speech enhancement algorithms have found many applications in mobile communications and human-machine interfaces. Although numerous algorithms are available and significant improvements have been obtained there is no single algorithm which suits all kinds of applications. Even for a single application such as low bit rate speech coding Accardi and Cox [1] proposed to use more than one estimator in order to deliver optimally preprocessed signals to the various parts of the speech coder, In this context they developed the notion of “core estimators”. They used a MMSE-LSA estimator [4] as a core estimator to enhance the prediction residual and an estimator for the magnitude-squared DFT coefficients to enhance the autocorrelation coefficients which are in turn used to compute the LSF coefficients. In this paper we focus on the estimation of the magnitude-squared DFT coefficients, however with a significantly improved statistical model.