Speech enhancement as a functional approximation and generalization

Noise reduction is used to reduce the noise effect on speech, and is important for many real speech applications. However, noise reduction inevitably causes speech distortion. The trade-off between noise reduction and speech distortion is always a key concern in designing noise reduction algorithms. In this study, we took a new look at this problem, and regarded the speech estimation as a functional approximation problem which was concerned with the approximation error and generalization ability (or complexity). In order to get a good generalization ability, a regularization framework was adopted which gave a constraint on the approximation function with certain smoothness. Moreover, the approximation function was selected in a reproducing kernel Hilbert space (RKHS). By this selection, a nonlinear mapping function could be incorporated in the approximation function with the application of the kernel trick. This approximation could explore the nonlinear and high-order statistical structure of speech which was different from traditional methods that only explore the linear and low-order statistical information of speech. By real simulations, we showed that (1) incorporating nonlinearity in the mapping function could bring better representational ability of the approximation function, hence a better trade-off between noise reduction and speech distortion than that of using a linear mapping function, and (2) a better speech enhancement performance than that of a compared classical speech enhancement method on the basis of segmental signal to noise ratio improvement and log spectral distance measurement.