Information-Geometric Optimization for Nonlinear Noise Reduction Systems

In this paper, we introduce an optimization theory of nonlinear noise reduction with a perfectly musical-noise-free property. To achieve high-quality noise reduction, an iterative spectral subtraction method, i.e., recursively applied weak nonlinear signal processing, has been proposed. Although evaluation experiments indicated the existence of an appropriate parameter setting that gives a musical-noise-free state, no theoretical studies have been carried out so far. Therefore, first, we theoretically derive parameters that satisfy the musical-noise-free condition by analysis based on higher-order statistics. It is clarified that finding a fixed point in the kurtosis of noise spectra enables the reproduction of the musical-noise-free state. Next, we derive a musical-noise-free condition in iterative Wiener filtering. Also, we provide an analogical perspective between the musical-noise-free noise reduction algorithm and the conventional information-geometric optimization theory. Finally, comparative experiments with commonly used noise reduction methods show the efficacy of the proposed method.