This article addresses the problem of multichannel audio source separation. We propose a framework where deep neural networks (DNNs) are used to model the source spectra and combined with the classical multichannel Gaussian model to exploit the spatial information. The parameters are estimated in an iterative expectation-maximization (EM) fashion and used to derive a multichannel Wiener filter. We present an extensive experimental study to show the impact of different design choices on the performance of the proposed technique. We consider different cost functions for the training of DNNs, namely the probabilistically motivated Itakura-Saito divergence, and also Kullback-Leibler, Cauchy, mean squared error, and phase-sensitive cost functions. We also study the number of EM iterations and the use of multiple DNNs, where each DNN aims to improve the spectra estimated by the preceding EM iteration. Finally, we present its application to a speech enhancement problem. The experimental results show the benefit of the proposed multichannel approach over a single-channel DNNbased approach and the conventional multichannel nonnegative matrix factorization based iterative EM algorithm.

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This paper describes a computationally-efficient blind source separation (BSS) method based on the independence, lowrankness, and directivity of the sources. A typical approach to BSS is unsupervised learning of a probabilistic model that consists of a source model representing the time-frequency structure of source images and a spatial model representing their interchannel covariance structure. Building upon the low-rank source model based on nonnegative matrix factorization (NMF), which has been considered to be effective for inter-frequency source alignment, multichannel NMF (MNMF) assumes source images to follow multivariate complex Gaussian distributions with unconstrained full-rank spatial covariance matrices (SCMs). An effective way of reducing the computational cost and initialization sensitivity of MNMF is to restrict the degree of freedom of SCMs. While a variant of MNMF called independent low-rank matrix analysis (ILRMA) severely restricts SCMs to rank-1 matrices under an idealized condition that only directional and lessechoic sources exist, we restrict SCMs to jointly-diagonalizable yet full-rank matrices in a frequency-wise manner, resulting in FastMNMF1. To help inter-frequency source alignment, we then propose FastMNMF2 that shares the directional feature of each source over all frequency bins. To explicitly consider the directivity or diffuseness of each source, we also propose rankconstrained FastMNMF that enables us to individually specify the ranks of SCMs. Our experiments showed the superiority of FastMNMF over MNMF and ILRMA in speech separation and the effectiveness of the rank constraint in speech enhancement.

This article addresses the problem of multichannel music separation. We propose a framework where the source spectra are estimated using deep neural networks and combined with spatial covariance matrices to encode the source spatial characteristics. The parameters are estimated in an iterative expectation-maximization fashion and used to derive a multichannel Wiener filter. We evaluate the proposed framework for the task of music separation on a large dataset. Experimental results show that the method we describe performs consistently well in separating singing voice and other instruments from realistic musical mixtures.

We consider the problem of robust automatic speech recognition (ASR) in the context of the CHiME-3 Challenge. The proposed system combines three contributions. First, we propose a deep neural network (DNN) based multichannel speech enhancement technique, where the speech and noise spectra are estimated using a DNN based regressor and the spatial parameters are derived in an expectation-maximization (EM) like fashion. Second, a conditional restricted Boltzmann machine (CRBM) model is trained using the obtained enhanced speech and used to generate simulated training and development datasets. The goal is to increase the similarity between simulated and real data, so as to increase the benefit of multicondition training. Finally, we make some changes to the ASR backend. Our system ranked 4th among 25 entries.

This paper describes a versatile method that accelerates multichannel source separation methods based on full-rank spatial modeling. A popular approach to multichannel source separation is to integrate a spatial model with a source model for estimating the spatial covariance matrices (SCMs) and power spectral densities (PSDs) of each sound source in the time-frequency domain. One of the most successful examples of this approach is multichannel nonnegative matrix factorization (MNMF) based on a full-rank spatial model and a low-rank source model. MNMF, however, is computationally expensive and often works poorly due to the difficulty of estimating the unconstrained full-rank SCMs. Instead of restricting the SCMs to rank-1 matrices with the severe loss of the spatial modeling ability as in independent low-rank matrix analysis (ILRMA), we restrict the SCMs of each frequency bin to jointly-diagonalizable but still full-rank matrices. For such a fast version of MNMF, we propose a computationally-efficient and convergence-guaranteed algorithm that is similar in form to that of ILRMA. Similarly, we propose a fast version of a stateof-the-art speech enhancement method based on a deep speech model and a low-rank noise model. Experimental results showed that the fast versions of MNMF and the deep speech enhancement method were several times faster and performed even better than the original versions of those methods, respectively.

This paper describes a semi-supervised multichannel speech enhancement method that uses clean speech data for prior training. Although multichannel nonnegative matrix factorization (MNMF) and its constrained variant called independent low-rank matrix analysis (ILRMA) have successfully been used for unsupervised speech enhancement, the low-rank assumption on the power spectral densities (PSDs) of all sources (speech and noise) does not hold in reality. To solve this problem, we replace a low-rank speech model with a deep generative speech model, i.e., formulate a probabilistic model of noisy speech by integrating a deep speech model, a low-rank noise model, and a full-rank or rank-1 model of spatial characteristics of speech and noise. The deep speech model is trained from clean speech data in an unsupervised auto-encoding variational Bayesian manner. Given multichannel noisy speech spectra, the full-rank or rank-1 spatial covariance matrices and PSDs of speech and noise are estimated in an unsupervised maximum-likelihood manner. Experimental results showed that the full-rank version of the proposed method was significantly better than MNMF, ILRMA, and the rank-1 version. We confirmed that the initialization-sensitivity and local-optimum problems of MNMF with many spatial parameters can be solved by incorporating the precise speech model.

This paper describes a joint blind source separation and dereverberation method that works adaptively and efficiently in a reverberant noisy environment. The modern approach to blind source separation (BSS) is to formulate a probabilistic model of multichannel mixture signals that consists of a source model representing the timefrequency structures of source spectrograms and a spatial model representing the inter-channel covariance structures of source images. The cutting-edge BSS method in this thread of research is fast multichannel nonnegative matrix factorization (FastMNMF) that consists of a low-rank source model based on nonnegative matrix factorization (NMF) and a full-rank spatial model based on jointly-diagonalizable spatial covariance matrices. Although FastMNMF is computationally efficient and can deal with both directional sources and diffuse noise simultaneously, its performance is severely degraded in a reverberant environment. To solve this problem, we propose autoregressive FastMNMF (AR-FastMNMF) based on a unified probabilistic model that combines FastMNMF with a blind dereverberation method called weighted prediction error (WPE), where all the parameters are optimized jointly such that the likelihood for observed reverberant mixture signals is maximized. Experimental results showed the superiority of AR-FastMNMF over conventional methods that perform blind dereverberation and BSS jointly or sequentially.