In this paper, we address a statistical model extension of multichannel nonnegative matrix factorization (MNMF) for blind source separation, and we propose a new parameter update algorithm used in the sub-Gaussian model. MNMF employs full-rank spatial covariance matrices and can simulate situations in which the reverberation is strong and the sources are not point sources. In conventional MNMF, spectrograms of observed signals are assumed to follow a multivariate Gaussian distribution. In this paper, first, to extend the MNMF model, we introduce the multivariate generalized Gaussian distribution as the multivariate sub-Gaussian distribution. Since the cost function of MNMF based on this multivariate sub-Gaussian model is difficult to minimize, we additionally introduce the joint-diagonalizability constraint in spatial covariance matrices to MNMF similarly to FastMNMF, and transform the cost function to the form to which we can apply the auxiliary functions to derive the valid parameter update rules. Finally, from blind source separation experiments, we show that the proposed method outperforms the conventional methods in source-separation accuracy.

中文翻译：

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基于多元复次高斯分布的联合对角化约束多通道非负矩阵分解

在本文中，我们解决了用于盲源分离的多通道非负矩阵分解 (MNMF) 的统计模型扩展，并提出了一种用于亚高斯模型的新参数更新算法。MNMF 采用满秩空间协方差矩阵，可以模拟混响强且源不是点源的情况。在传统的 MNMF 中，假设观测信号的频谱图遵循多元高斯分布。在本文中，首先，为了扩展MNMF模型，我们引入多元广义高斯分布作为多元亚高斯分布。由于基于这种多元亚高斯模型的 MNMF 的成本函数难以最小化，我们另外将空间协方差矩阵中的联合对角化约束引入 MNMF，类似于 FastMNMF，并将成本函数转换为我们可以应用辅助函数来推导出有效参数更新规则的形式。最后，从盲源分离实验中，我们表明所提出的方法在源分离精度方面优于传统方法。