This paper describes multichannel speech enhancement for improving automatic speech recognition (ASR) in noisy environments. Recently, the minimum variance distortionless response (MVDR) beamforming has widely been used because it works well if the steering vector of speech and the spatial covariance matrix (SCM) of noise are given. To estimating such spatial information, conventional studies take a supervised approach that classifies each time-frequency (TF) bin into noise or speech by training a deep neural network (DNN). The performance of ASR, however, is degraded in an unknown noisy environment. To solve this problem, we take an unsupervised approach that decomposes each TF bin into the sum of speech and noise by using multichannel nonnegative matrix factorization (MNMF). This enables us to accurately estimate the SCMs of speech and noise not from observed noisy mixtures but from separated speech and noise components. In this paper, we propose online MVDR beamforming by effectively initializing and incrementally updating the parameters of MNMF. Another main contribution is to comprehensively investigate the performances of ASR obtained by various types of spatial filters, i.e., time-invariant and variant versions of MVDR beamformers and those of rank-1 and full-rank multichannel Wiener filters, in combination with MNMF. The experimental results showed that the proposed method outperformed the state-of-the-art DNN-based beamforming method in unknown environments that did not match training data.
Multichannel extensions of NMF @cite_35 @cite_27 @cite_10 @cite_0 @cite_29 @cite_1 represent the complex spectrograms of multichannel mixture signals by using the SCMs and low-rank power spectrograms of multiple source signals. Ozerov et al. @cite_27 pioneered the use of NMF for multichannel source separation, where the SCMs are restricted to rank-1 matrices and the cost function based on the Itakura-Saito (IS) divergence is minimized. This model was extended to have full-rank SCMs @cite_10 . Sawada et al. @cite_8 introduced partitioning parameters to have a set of basis spectra shared by all sources and derived a majorization-minimization (MM) algorithm. Nikunen and Virtanen @cite_29 proposed a similar model that represents the SCM of each source as the weighted sum of direction-dependent SCMs. While these methods can be used in a underdetermined case, Kitamura et al. @cite_1 proposed independent low-rank matrix analysis (ILRMA) for a determined case by restricting the SCMs of @cite_8 to rank-1 matrices. This can be viewed as a unified model of NMF and independent vector analysis (IVA) and is robust to initialization.
@cite_35 @cite_8 @cite_29 @cite_1 @cite_0 @cite_27 @cite_10
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This paper presents new statistical methods of multichannel audio source separation based on unified source and spatial models that, respectively, represent the generative process of latent source spectrograms and that of observed mixture spectrograms. One possibility of the source model is a factor model based on nonnegative matrix factorization that represents each time-frequency (TF) bin as the weighted sum of basis spectra. Another possibility is a mixture model inspired by latent Dirichlet allocation that exclusively classifies each TF bin into one of basis spectra. Similarly, the spatial model can either be a factor model that represents each TF bin as the weighted sum of source spectra or a mixture model that classifies each bin into one of those spectra. To unify these models in a principled manner and incorporate prior knowledge of a microphone array, we propose hierarchical Bayesian models of all the source–spatial combinations (factor–factor, mixture–factor, factor–mixture, and mixture–mixture models) and derive efficient Gibbs sampling algorithms for posterior inference. Experimental results showed that the proposed unified models outperformed the state-of-the-art method using only the spatial mixture model. Among the four unified models, the spatial factor model tended to work better than the spatial mixture model in exchange for larger computational cost, and the choice of source models had a little impact on the performance and computational cost. This paper presents new formulations and algorithms for multichannel extensions of non-negative matrix factorization (NMF). The formulations employ Hermitian positive semidefinite matrices to represent a multichannel version of non-negative elements. Multichannel Euclidean distance and multichannel Itakura-Saito (IS) divergence are defined based on appropriate statistical models utilizing multivariate complex Gaussian distributions. To minimize this distance divergence, efficient optimization algorithms in the form of multiplicative updates are derived by using properly designed auxiliary functions. Two methods are proposed for clustering NMF bases according to the estimated spatial property. Convolutive blind source separation (BSS) is performed by the multichannel extensions of NMF with the clustering mechanism. Experimental results show that 1) the derived multiplicative update rules exhibited good convergence behavior, and 2) BSS tasks for several music sources with two microphones and three instrumental parts were evaluated successfully. This paper addresses the problem of sound source separation from a multichannel microphone array capture via estimation of source spatial covariance matrix (SCM) of a short-time Fourier transformed mixture signal. In many conventional audio separation algorithms the source mixing parameter estimation is done separately for each frequency thus making them prone to errors and leading to suboptimal source estimates. In this paper we propose a SCM model which consists of a weighted sum of direction of arrival (DoA) kernels and estimate only the weights dependent on the source directions. In the proposed algorithm, the spatial properties of the sources become jointly optimized over all frequencies, leading to more coherent source estimates and mitigating the effect of spatial aliasing at high frequencies. The proposed SCM model is combined with a linear model for magnitudes and the parameter estimation is formulated in a complex-valued non-negative matrix factorization (CNMF) framework. Simulations consist of recordings done with a hand-held device sized array having multiple microphones embedded inside the device casing. Separation quality of the proposed algorithm is shown to exceed the performance of existing state of the art separation methods with two sources when evaluated by objective separation quality metrics. This paper addresses the determined blind source separation problem and proposes a new effective method unifying independent vector analysis (IVA) and nonnegative matrix factorization (NMF). IVA is a state-of-the-art technique that utilizes the statistical independence between sources in a mixture signal, and an efficient optimization scheme has been proposed for IVA. However, since the source model in IVA is based on a spherical multivariate distribution, IVA cannot utilize specific spectral structures such as the harmonic structures of pitched instrumental sounds. To solve this problem, we introduce NMF decomposition as the source model in IVA to capture the spectral structures. The formulation of the proposed method is derived from conventional multichannel NMF (MNMF), which reveals the relationship between MNMF and IVA. The proposed method can be optimized by the update rules of IVA and single-channel NMF. Experimental results show the efficacy of the proposed method compared with IVA and MNMF in terms of separation accuracy and convergence speed. We consider inference in a general data-driven object-based model of multichannel audio data, assumed generated as a possibly underdetermined convolutive mixture of source signals. We work in the short-time Fourier transform (STFT) domain, where convolution is routinely approximated as linear instantaneous mixing in each frequency band. Each source STFT is given a model inspired from nonnegative matrix factorization (NMF) with the Itakura-Saito divergence, which underlies a statistical model of superimposed Gaussian components. We address estimation of the mixing and source parameters using two methods. The first one consists of maximizing the exact joint likelihood of the multichannel data using an expectation-maximization (EM) algorithm. The second method consists of maximizing the sum of individual likelihoods of all channels using a multiplicative update algorithm inspired from NMF methodology. Our decomposition algorithms are applied to stereo audio source separation in various settings, covering blind and supervised separation, music and speech sources, synthetic instantaneous and convolutive mixtures, as well as professionally produced music recordings. Our EM method produces competitive results with respect to state-of-the-art as illustrated on two tasks from the international Signal Separation Evaluation Campaign (SiSEC 2008). We address the problem of blind audio source separation in the under-determined and convolutive case. The contribution of each source to the mixture channels in the time-frequency domain is modeled by a zero-mean Gaussian random vector with a full rank covariance matrix composed of two terms: a variance which represents the spectral properties of the source and which is modeled by a nonnegative matrix factorization (NMF) model and another full rank covariance matrix which encodes the spatial properties of the source contribution in the mixture. We address the estimation of these parameters by maximizing the likelihood of the mixture using an expectation-maximization (EM) algorithm. Theoretical propositions are corroborated by experimental studies on stereo reverberant music mixtures.