Controlling Tradeoff Between Approximation Accuracy and Complexity of a Smooth Function in a Reproducing Kernel Hilbert Space for Noise Reduction

Noise reduction algorithms are widely used to mitigate noise effects on speech to improve the robustness of speech technology applications. However, they inevitably cause speech distortion. The tradeoff between noise reduction and speech distortion is a key concern in designing noise reduction algorithms. This study proposes a novel framework for noise reduction by considering this tradeoff. We regard speech estimation as a function approximation problem in a regularized reproducing kernel Hilbert space (RKHS). In the estimation, the objective function is formulated to find an approximation function by controlling the tradeoff between approximation accuracy and function complexity. For noisy observations, this is equivalent to controlling the tradeoff between noise reduction and speech distortion. Since the target function is approximated in an RKHS, either a linear or nonlinear mapping function can be naturally incorporated in the estimation by a kernel trick. Traditional signal subspace and Wiener filtering based noise reduction can be derived as special cases when a linear kernel function is applied in this framework. We first provided a theoretical analysis of the tradeoff property of the framework in noise reduction. Then we applied our proposed noise reduction method in speech enhancement and noisy robust speech recognition experiments. Compared to several classical noise reduction methods, our proposed method showed promising advantages.