Theoretical analysis of iterative weak spectral subtraction via higher-order statistics

In this paper, we provide a new theoretical analysis of the amount of musical noise generated via iterative spectral subtraction based on higher-order statistics. To achieve high-quality noise reduction with low musical noise, the iterative spectral subtraction method, i.e., recursively applied weak nonlinear signal processing, has been proposed. Although the effectiveness of the method has been reported experimentally, there have been no theoretical studies. Therefore, in this paper, we formulate the generation process of musical noise by tracing the change in kurtosis, and conduct a comparison of the amount of musical noise for different parameter settings under the same noise reduction performance. It is clarified from mathematical analysis and evaluation experiments that iterative spectral subtraction with very weak processing can result in the generation of less musical noise.