Laplace Nonnegative Matrix Factorization with Application to Semi-supervised Audio Denoising

This paper proposes two statistical models for the nonnegative matrix factorization (NMF) based on heavy-tailed distributions. In the NMF for acoustic signals, previous works justify the additivity of an observed spectrogram using the reproductive property of a probability density function. However, the effectiveness of these properties is not clear. Consequently, to construct a model robust to noise, statistical models based on heavy-tailed distributions are recently growing up. In this paper, as heavy-tailed models for the NMF, we introduce statistical models based on the complex Laplace distributions, and call them Laplace-NMF. Moreover, we derive convergence-guaranteed optimization algorithms to estimate parameters. From our formulation, a statistical interpretation of the Itakura-Saito (IS) divergence-based NMF is newly revealed. We confirm the effectiveness of Laplace-NMF in semi-supervised audio denoising.