Joint-Diagonalizability-Constrained Multichannel Nonnegative Matrix Factorization Based on Multivariate Complex Sub-Gaussian Distribution

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.Comment: 5 pages, 3 figures, To appear in the Proceedings of the 28th European Signal Processing Conference (EUSIPCO 2020). arXiv admin note: text overlap with arXiv:2002.0057

Consistent Independent Low-Rank Matrix Analysis for Determined Blind Source Separation

Independent low-rank matrix analysis (ILRMA) is the state-of-the-art algorithm for blind source separation (BSS) in the determined situation (the number of microphones is greater than or equal to that of source signals). ILRMA achieves a great separation performance by modeling the power spectrograms of the source signals via the nonnegative matrix factorization (NMF). Such a highly developed source model can solve the permutation problem of the frequency-domain BSS to a large extent, which is the reason for the excellence of ILRMA. In this paper, we further improve the separation performance of ILRMA by additionally considering the general structure of spectrograms, which is called consistency, and hence we call the proposed method Consistent ILRMA. Since a spectrogram is calculated by an overlapping window (and a window function induces spectral smearing called main- and side-lobes), the time-frequency bins depend on each other. In other words, the time-frequency components are related to each other via the uncertainty principle. Such co-occurrence among the spectral components can function as an assistant for solving the permutation problem, which has been demonstrated by a recent study. On the basis of these facts, we propose an algorithm for realizing Consistent ILRMA by slightly modifying the original algorithm. Its performance was extensively evaluated through experiments performed with various window lengths and shift lengths. The results indicated several tendencies of the original and proposed ILRMA that include some topics not fully discussed in the literature. For example, the proposed Consistent ILRMA tends to outperform the original ILRMA when the window length is sufficiently long compared to the reverberation time of the mixing system.Comment: Submitted to EURASIP J. Adv. Signal. Process. Accepted on Oct. 30, 202