Mathematical metric of amount of musical noise in recursive spectral subtraction

摘要

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 generationof less musical noise.%本稿では，反復型スペクトル減算法に関して，高次統計量に基づくミュージカルノイズ評価尺度を用いた理論解析を行った結果を述べる．現在，ミュージカルノイズ発生量を抑えつつ高い雑音抑圧性能を達成できる反復型スペクトル減算法が提案されており，この手法の有効性は実験的に示されているが，理論的な研究は未だに成されていない．そこで，本稿では，尖魔の変化を追うことで反復ごとのミュージカルノイズの発生過程を定式化し，等雑音抑圧量下で，異なるパラメータで処理を行った場合のミュージカルノイズの発生量の比較を行った．この理論解析および評価実験より，非常に弱い処理を繰り返す場合の反復型スペクトル減算法はミュージカルノイズ低減の効果があることが明らかになった．