Independent Low-rank Matrix Analysis Research Articles

Determined Blind Source Separation Combining Independent Low-rank Matrix Analysis with Optimized Parameters and Q-learning

Determined Blind Source Separation Combining Independent Low-rank Matrix Analysis with Optimized Parameters and Q-learning

Semi-blind source separation using convolutive transfer function for nonlinear acoustic echo cancellation.

The recently proposed semi-blind source separation (SBSS) method for nonlinear acoustic echo cancellation (NAEC) outperforms adaptive NAEC in attenuating the nonlinear acoustic echo. However, the multiplicative transfer function (MTF) approximation makes it unsuitable for real-time applications, especially in highly reverberant environments, and the natural gradient makes it hard to balance well between fast convergence speed and stability. In this paper, two more effective SBSS methods based on auxiliary-function-based independent vector analysis (AuxIVA) and independent low-rank matrix analysis (ILRMA) are proposed. The convolutive transfer function approximation is used instead of the MTF so that a long impulse response can be modeled with a short latency. The optimization schemes used in AuxIVA and ILRMA are carefully regularized according to the constrained demixing matrix of NAEC. The experimental results validate significantly better echo cancellation performances of the proposed methods.

Repeated Update of Demixing Vectors in Independent Low-rank Matrix Analysis for Better Separation

Repeated Update of Demixing Vectors in Independent Low-rank Matrix Analysis for Better Separation

Deficient-basis-complementary rank-constrained spatial covariance matrix estimation based on multivariate generalized Gaussian distribution for blind speech extraction

Rank-constrained spatial covariance matrix estimation (RCSCME) is a blind speech extraction method utilized under the condition that one-directional target speech and diffuse background noise are mixed. In this paper, we propose a new model extension of RCSCME. RCSCME simultaneously conducts both the deficient rank-1 component complementation of the diffuse noise spatial covariance matrix, which is incompletely estimated by preprocessing methods such as independent low-rank matrix analysis, and the estimation of the source model parameters. In the conventional RCSCME, between the two parameters constituting the deficient rank-1 component, only the scale is estimated, whereas the other parameter, the deficient basis, is fixed in advance; however, how to choose the fixed deficient basis is not unique. In the proposed RCSCME model, we also regard the deficient basis as a parameter to estimate. As the generative model of an observed signal, we utilized the super-Gaussian generalized Gaussian distribution, which achieves better separation performance than the Gaussian distribution in the conventional RCSCME. Assuming the model, we derive new majorization-minimization (MM)- and majorization-equalization (ME)-algorithm-based update rules for the deficient basis. In particular, among innumerable ME-algorithm-based update rules, we successfully find an ME-algorithm-based update rule with a mathematical proof supporting the fact that the step of the update rule is larger than that of the MM-algorithm-based update rule. We confirm that the proposed method outperforms conventional methods under several simulated noise conditions and a real noise condition.

Convolutive Transfer Function-Based Multichannel Nonnegative Matrix Factorization for Overdetermined Blind Source Separation

Most multichannel blind source separation (BSS) approaches rely on a spatial model to encode the transfer functions from sources to microphones and a source model to encode the source power spectral density. The rank-1 spatial model has been widely exploited in independent component analysis (ICA), independent vector analysis (IVA), and independent low-rank matrix analysis (ILRMA). The full-rank spatial model is also considered in many BSS approaches, such as full-rank spatial covariance matrix analysis (FCA), multichannel nonnegative matrix factorization (MNMF), and FastMNMF, which can improve the separation performance in the case of long reverberation times. This paper proposes a new MNMF framework based on the convolutive transfer function (CTF) for overdetermined BSS. The time-domain convolutive mixture model is approximated by a frequency-wise convolutive mixture model instead of the widely adopted frequency-wise instantaneous mixture model. The iterative projection algorithm is adopted to estimate the demixing matrix, and the multiplicative update rule is employed to estimate nonnegative matrix factorization (NMF) parameters. Finally, the source image is reconstructed using a multichannel Wiener filter. The advantages of the proposed method are twofold. First, the CTF approximation enables us to use a short window to represent long impulse responses. Second, the full-rank spatial model can be derived based on the CTF approximation and slowly time-variant source variances, and close relationships between the proposed method and ILRMA, FCA, MNMF and FastMNMF are revealed. Extensive experiments show that the proposed algorithm achieves a higher separation performance than ILRMA and FastMNMF in reverberant environments.

Computationally-Efficient Overdetermined Blind Source Separation Based on Iterative Source Steering

This paper describesa computationally-efficient optimization algorithm for the blind source separation (BSS) of overdetermined mixtures. In the determined case, a matrix-inversion-free iterative source steering (ISS) algorithm has been proposed for estimating a square demixing matrix as a computationally-efficient alternative to the popular iterative projection (IP) algorithm. The IP algorithm is based on source-wise (i.e., row-wise) updates of the demixing matrix, and lends itself naturally to an extension to overdetermined independent vector analysis (IVA) called OverIVA. In contrast, the ISS algorithm changes the whole demixing matrix at every update, making its extension to the overdetermined case non-trivial. In this paper, we propose a modified ISS algorithm for OverIVA fully exploiting the computational savings of ISS. We also derive an overdetermined extension of independent low-rank matrix analysis (OverILRMA) with the modified ISS algorithm. Experimental results showed that the proposed ISS-based OverIVA and OverILRMA were comparable or superior to the conventional IP-based counterparts in speech separation performance while achieving lower computational cost.

Interactive speech source separation based on independent low-rank matrix analysis

Interactive speech source separation based on independent low-rank matrix analysis

Minimum-Volume Multichannel Nonnegative Matrix Factorization for Blind Audio Source Separation

Multichannel blind audio source separation aims to recover the latent sources from their multichannel mixtures without supervised information. One state-of-the-art blind audio source separation method, named independent low-rank matrix analysis (ILRMA), unifies independent vector analysis (IVA) and nonnegative matrix factorization (NMF). However, the spectra matrix produced from NMF may not find a compact spectral basis. It may not guarantee the identifiability of each source as well. To address this problem, here we propose to enhance the identifiability of the source model by a minimum-volume prior distribution. We further regularize a multichannel NMF (MNMF) and ILRMA respectively with the minimum-volume regularizer. The proposed methods maximize the posterior distribution of the separated sources, which ensures the stability of the convergence. Experimental results demonstrate the effectiveness of the proposed methods compared with auxiliary independent vector analysis, MNMF, ILRMA and its extensions. The source code is available at https://github.com/alexwang9654/m-ILRMA .

Determined BSS Based on Time-Frequency Masking and Its Application to Harmonic Vector Analysis

This paper proposes harmonic vector analysis (HVA) based on a general algorithmic framework of audio blind source separation (BSS) that is also presented in this paper. BSS for a convolutive audio mixture is usually performed by multichannel linear filtering when the numbers of microphones and sources are equal (determined situation). This paper addresses such determined BSS based on batch processing. To estimate the demixing filters, effective modeling of the source signals is important. One successful example is independent vector analysis (IVA) that models the signals via co-occurrence among the frequency components in each source. To give more freedom to the source modeling, a general framework of determined BSS is presented in this paper. It is based on the plug-and-play scheme using a primal-dual splitting algorithm and enables us to model the source signals implicitly through a time-frequency mask. By using the proposed framework, determined BSS algorithms can be developed by designing masks that enhance the source signals. As an example of its application, we propose HVA by defining a time-frequency mask that enhances the harmonic structure of audio signals via sparsity of cepstrum. The experiments showed that HVA outperforms IVA and independent low-rank matrix analysis (ILRMA) for both speech and music signals. A MATLAB code is provided along with the paper for a reference.

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.

Independent Low-Rank Matrix Analysis-Based Automatic Artifact Reduction Technique Applied to Three BCI Paradigms.

Electroencephalogram (EEG)-based brain-computer interfaces (BCIs) can potentially enable people to non-invasively and directly communicate with others using brain activities. Artifacts generated from body activities (e.g., eyeblinks and teeth clenches) often contaminate EEGs and make EEG-based classification/identification hard. Although independent component analysis (ICA) is the gold-standard technique for attenuating the effects of such contamination, the estimated independent components are still mixed with artifactual and neuronal information because ICA relies only on the independence assumption. The same problem occurs when using independent vector analysis (IVA), an extended ICA method. To solve this problem, we designed an independent low-rank matrix analysis (ILRMA)-based automatic artifact reduction technique that clearly models sources from observations under the independence assumption and a low-rank nature in the frequency domain. For automatic artifact reduction, we combined the signal separation technique with an independent component classifier for EEGs named ICLabel. To assess the comparative efficiency of the proposed method, the discriminabilities of artifact-reduced EEGs using ICA, IVA, and ILRMA were determined using an open-access EEG dataset named OpenBMI, which contains EEG data obtained through three BCI paradigms [motor-imagery (MI), event-related potential (ERP), and steady-state visual evoked potential (SSVEP)]. BCI performances were obtained using these three paradigms after applying artifact reduction techniques, and the results suggested that our proposed method has the potential to achieve higher discriminability than ICA and IVA for BCIs. In addition, artifact reduction using the ILRMA approach clearly improved (by over 70%) the averaged BCI performances using artifact-reduced data sufficiently for most needs of the BCI community. The extension of ICA families to supervised separation that leaves the discriminative ability would further improve the usability of BCIs for real-life environments in which artifacts frequently contaminate EEGs.

Fast Multichannel Nonnegative Matrix Factorization With Directivity-Aware Jointly-Diagonalizable Spatial Covariance Matrices for Blind Source Separation

This article describes a computationally-efficient blind source separation (BSS) method based on the independence, low-rankness, 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 inter-channel 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 less-echoic 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 rank-constrained 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.

Independent Low-Rank Matrix Analysis Based on Time-Variant Sub-Gaussian Source Model for Determined Blind Source Separation

Independent low-rank matrix analysis (ILRMA) is a fast and stable method of blind audio source separation. Conventional ILRMAs assume time-variant (super-)Gaussian source models, which can only represent signals that follow a super-Gaussian distribution. In this article, we focus on ILRMA based on a generalized Gaussian distribution (GGD-ILRMA) and propose a new type of GGD-ILRMA that adopts a time-variant sub-Gaussian distribution for the source model. We propose a new update scheme called generalized iterative projection for homogeneous source models (GIP-HSM) and obtain a convergence-guaranteed update rule for demixing spatial parameters by combining the GIP-HSM scheme and the majorization-minimization (MM) algorithm. Furthermore, a new extension of the MM algorithm is proposed for the convergence acceleration by applying the majorization-equalization algorithm to a multivariate case. In the experimental evaluation, we show the versatility of the proposed method, i.e., the proposed time-variant sub-Gaussian source model can be applied to various types of source signal.

Blind Speech Extraction Based on Rank-Constrained Spatial Covariance Matrix Estimation With Multivariate Generalized Gaussian Distribution

In this article, we propose a new blind speech extraction (BSE) method that robustly extracts a directional speech from background diffuse noise by combining independent low-rank matrix analysis (ILRMA) and efficient rank-constrained spatial covariance matrix (SCM) estimation. To achieve more accurate BSE than ILRMA, which assumes each source to be a point source (rank-1 spatial model), the proposed method restores the lost spatial basis for the full-rank SCM of diffuse noise. We adopt the multivariate complex generalized Gaussian distribution (GGD) as the statistical generative model to express various types of observed signal. To estimate the model parameters for an arbitrary shape parameter of the multivariate GGD, we derive a new inequality for rank-constrained SCMs. Also, we propose new acceleration methods to accomplish much faster extraction than conventional blind source separation methods. In BSE experiments using simulated and real recorded data, we confirm that the proposed method achieves more accurate and faster speech extraction than conventional methods.

Auxiliary-Function-Based Independent Vector Analysis Using Generalized Inter-Clique Dependence Source Models With Clique Variance Estimation

By introducing a frequency dependence source prior including full-band and clique models, independent vector analysis (IVA) has been successfully used for convolutive blind source separation (BSS). In addition, independent low-rank matrix analysis (ILRMA) learns a low-rank approximation of the time-frequency structure of source signals. This paper presents IVA using a clique-based frequency dependence model with time-varying clique variances to combine advantages of both ILRMA and clique-model-based IVA for BSS of speech signals. Although conventional clique models are effective in separating sources with specific spectral structures, the dependency among the cliques is considered by overlaps between cliques or a global clique of all frequency bins if there is. To avoid the permutation problem by strengthening the dependency among the cliques, we develop a generalized probability-density-function (pdf) model imposing a variable exponent on the summed cliques with overlaps and time-varying clique variances, which may include most conventional source models as particular cases. In addition, update rules of the clique variances and demixing matrices are derived by minimization of the cost function of BSS as well as non-negative matrix factorization (NMF) and auxiliary function techniques for fast and robust convergence, respectively. Through experiments on BSS of speech mixtures with various mixing conditions, the proposed IVA showed improved separation performance than the conventional methods. Experimental results consistently demonstrated that the performance of a method could be determined in general by the trade-off between the degree of freedom of source models (as long as model parameters were accurately estimated) and the vulnerability to the permutation problem.

Semi-Supervised Multichannel Speech Enhancement With a Deep Speech Prior

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.

Underdetermined Source Separation Based on Generalized Multichannel Variational Autoencoder

This paper deals with a multichannel audio source separation problem under underdetermined conditions. Multichannel non-negative matrix factorization (MNMF) is a powerful method for underdetermined audio source separation, which adopts the NMF concept to model and estimate the power spectrograms of the sound sources in a mixture signal. This concept is also used in independent low-rank matrix analysis (ILRMA), a special class of the MNMF formulated under determined conditions. While these methods work reasonably well for particular types of sound sources, one limitation is that they can fail to work for sources with spectrograms that do not comply with the NMF model. To address this limitation, an extension of ILRMA called the multichannel variational autoencoder (MVAE) method was recently proposed, where a conditional VAE (CVAE) is used instead of the NMF model for expressing source power spectrograms. This approach has performed impressively in determined source separation tasks thanks to the representation power of deep neural networks. While the original MVAE method was formulated under determined mixing conditions, this paper proposes a generalized version of it by combining the ideas of MNMF and MVAE so that it can also deal with underdetermined cases. We call this method the generalized MVAE (GMVAE) method. In underdetermined source separation and speech enhancement experiments, the proposed method performed better than baseline methods.

A review of blind source separation methods: two converging routes to ILRMA originating from ICA and NMF

This paper describes several important methods for the blind source separation of audio signals in an integrated manner. Two historically developed routes are featured. One started from independent component analysis and evolved to independent vector analysis (IVA) by extending the notion of independence from a scalar to a vector. In the other route, nonnegative matrix factorization (NMF) has been extended to multichannel NMF (MNMF). As a convergence point of these two routes, independent low-rank matrix analysis has been proposed, which integrates IVA and MNMF in a clever way. All the objective functions in these methods are efficiently optimized by majorization-minimization algorithms with appropriately designed auxiliary functions. Experimental results for a simple two-source two-microphone case are given to illustrate the characteristics of these five methods.

Generalized independent low-rank matrix analysis using heavy-tailed distributions for blind source separation

In this paper, statistical-model generalizations of independent low-rank matrix analysis (ILRMA) are proposed for achieving high-quality blind source separation (BSS). BSS is a crucial problem in realizing many audio applications, where the audio sources must be separated using only the observed mixture signal. Many algorithms for solving BSS have been proposed, especially in the history of independent component analysis and nonnegative matrix factorization. In particular, ILRMA can achieve the highest separation performance for music or speech mixtures, where ILRMA assumes both independence between sources and the low-rankness of time-frequency structure in each source. In this paper, we propose two extensions of the source distribution assumed in ILRMA. We introduce a heavy-tailed property by replacing the conventional Gaussian source distribution with a generalized Gaussian or Student’s t distribution. Convergence-guaranteed efficient algorithms are derived for the proposed methods, and the relationship between the generalized Gaussian and Student’s t distributions in the source model estimation is revealed. By experimental evaluation, the validity of the heavy-tailed generalizations of ILRMA is confirmed.

Low Latency and High Quality Two-Stage Human-Voice-Enhancement System for a Hose-Shaped Rescue Robot

[abstFig src='/00290001/19.jpg' width='300' text='Human-voice enhancement system for a hose-shaped robot' ] This paper presents the design and implementation of a two-stage human-voice enhancement system for a hose-shaped rescue robot. When a microphone-equipped hose-shaped robot is used to search for a victim under a collapsed building, human-voice enhancement is crucial because the sound captured by a microphone array is contaminated by the ego-noise of the robot. For achieving both low latency and high quality, our system combines online and offline human-voice enhancement, providingan overview first and then details on demand. The online enhancement is used for searching for a victim in real time, while the offline one facilitates scrutiny by listening to highly enhanced human voices. Our online enhancement is based on an online robust principal component analysis, and our offline enhancement is based on an independent low-rank matrix analysis. The two enhancement methods are integrated with Robot Operating System (ROS). Experimental results showed that both the online and offline enhancement methods outperformed conventional methods.