Efficient Full-Rank Spatial Covariance Estimation Using Independent Low-Rank Matrix Analysis for Blind Source Separation

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.

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.

The issue of convolutive blind source separation (BSS) is addressed in this paper. Independent low-rank matrix analysis (ILRMA), unifying frequency-domain independent component analysis (FDICA) and nonnegative matrix factorization (NMF), is a method that has recently proposed to model low-rank structure of source spectra by using NMF in addition to independence between sources used in FDICA and independent vector analysis (IVA). Although ILRMA has been shown to provide better separation performance than FDICA and IVA, the frequency components of each source are assumed to be independent in ILRMA due to NMF modeling of source spectra, which may degrade its performance when the short-term Fourier transform (STFT) is unable to decorrelate the frequency components for each source. This paper therefore presents a new BSS method that unifies IVA and positive semidefinite tensor factorization (PSDTF). PSDTF models not only power spectra in the same way NMF does but also models the correlations between frequency bins in each source. The proposed method can be viewed as a multichannel extension of PSDTF and exploits both the independence between sources and the inter-frequency correlations as a clue for separating mixtures. Experimental results indicate the improved performance of our approach.

In the field of camera-based photoplethysmography the application of blind source separation (BSS) techniques has extensively stressed to cope with frequently occurring artifacts and noise. Although said techniques can help to extract the cardiac component from a mixture of input sources, permutation indeterminacy inherit to BSS techniques often introduces inaccuracies or requires manual intervention. The current contribution focuses on methods to automatically select the cardiac component from the output of BSS techniques applied to camera-based photoplethysmograms. To that end, we propose simple Markov models to describe and subsequently identify cardiac components. It is shown that good results can be obtained by combining different simple Markov models.

This paper addresses the determined convolutive blind source separation (BSS) problem. The state-of-the-art independent low-rank matrix analysis (ILRMA), unifying independent component analysis (ICA) and nonnegative matrix factorization, has the disadvantage of ignoring inter-frame and inter-frequency spectral correlation of source signals. We here propose a new BSS method that estimates a linear transformation for spectral decorrelation and performs ILRMA in the transformed domain. A newly introduced optimization problem is an extension of that for ICA based on maximum likelihood. For this problem, we provide a necessary and sufficient condition for the existence of optimal solutions, and develop algorithms based on block coordinate descent methods with closed-form solutions. Experimental results show the improved separation performance of the proposed method compared to ILRMA.

Signal estimation from functional magnetic resonance imaging data (fMRI) is a difficult and challenging task that involves carefully chosen models that can be validated by domain experts. Blind source separation (BSS) techniques such as principal component analysis (PCA), independent component analysis (ICA), and tensor decomposition have been proposed for estimating the task-fMRI signals. However, few studies have investigated their efficacy for classifying different tasks. This paper proposes yet another novel method to validate the signal estimation using predictive performance of the methods. Three commonly used BSS techniques are used for estimating signals (spatio-temporal maps) from task-fMRI. The dataset (consisting of 4 tasks) is taken from the Human Connectome Project (HCP). The extracted temporal signals are used to train a classifier that classifies two different tasks. For a binary classification, a Constrained-PARAFAC tensor decomposition achieves 92% accuracy for differentiating gambling vs. relational tasks. In addition, results for other binary task classifications are also presented. Overall, the proposed Constrained-PARAFAC performs better in prediction performance compared to PCA and ICA.

In inter-molecular multiple quantum coherences (iMQC) experiments, the iMQC signals is easily contaminated by the conventional single-quantum coherence (SQC) signals. How to get the pure iMQC signal is still an open problem for the nuclear magnetic resonance (NMR) scientists. A soft-separation method using blind source separation (BSS) technique was presented to attempt to resolve the problem for the first time. The performance of the three kinds of the different BSS techniques, algorithm for multiple unknown signals extraction (AMUSE), second order nonstationary source separation (SONS) and second order blind identification (SOBI), is evaluated. The numerical experiments show that they can separate intermolecular zero-quantum coherence (iZQC) signal very well.

Wide-area techniques provide a powerful tool to extract spatio-temporal patterns from high-dimensional datasets and can be used for event detection and visualization, data fusion, stability assessment, and coherency analysis. In this paper, a novel blind source separation-based approach for extracting low-frequency spatio-temporal patterns from measured ambient power system data is proposed and a spatio-temporal visualization index is also suggested. This methodology combines a nonlinear hierarchical neural network with a Blind Source Separation (BSS) technique. The neural network allows reducing noise and removing the nonlinear relations among data (preserve dynamic features of interest), while the BSS technique permits extracting spatial and temporal patterns. In addition, the proposed approach takes advantage of the latest techniques in nonlinear estimation of non-stationary time series. Finally, application examples of the proposed framework on real test cases recorded from an actual power system by Phasor Measurement Units (PMUs) are presented. The obtained results show that the temporal patterns can be used for extracting and identifying the low-frequency oscillation modes and the spatial patterns can be used for identifying modes with the most contribution in original data. Compared to other BSS approaches, the proposed method has shown to be better for the analysis of real ambient data.

We address the problem of Blind Source Separation (BSS) of superimposed signals in situations where one signal has constant or slowly varying intensities at some consecutive locations and at the corresponding locations the other signal has highly varying intensities. Independent Component Analysis (ICA) is a major technique for Blind Source Separation and the existing ICA algorithms fail to estimate the original intensities in the stated situation. We combine the advantages of existing sparse methods and Kernel ICA in our technique, by proposing wavelet packet based sparse decomposition of signals prior to the application of Kernel ICA. Simulations and experimental results illustrate the effectiveness and accuracy of the proposed approach. The approach is general in the way that it can be tailored and applied to a wide range of BSS problems concerning one-dimensional signals and images (two-dimensional signals).

We consider the problem of blind source separation of independent signals which passed through a multi-input multi-output linear time-invariant system. An approximate maximum likelihood estimator and its performance were studied by Yellin and Friedlander (see IEEE Trans. Signal Processing, vol.47, no.5, p.1410-14, 1999, and vol.47, no.6, p.1542-58). The results derived therein are used here to study the performance of source separation techniques based on high order statistics.

In graph signal processing (GSP), prior information on the dependencies in the signal is collected in a graph which is then used when processing or analyzing the signal. Blind source separation (BSS) techniques have been developed and analyzed in different domains, but for graph signals the research on BSS is still in its infancy. In this paper, this gap is filled with two contributions. First, a nonparametric BSS method, which is relevant to the GSP framework, is refined, the Cramér-Rao bound (CRB) for mixing and unmixing matrix estimators in the case of Gaussian moving average graph signals is derived, and for studying the achievability of the CRB, a new parametric method for BSS of Gaussian moving average graph signals is introduced. Second, we also consider BSS of non-Gaussian graph signals and two methods are proposed. Identifiability conditions show that utilizing both graph structure and non-Gaussianity provides a more robust approach than methods which are based on only either graph dependencies or non-Gaussianity. It is also demonstrated by numerical study that the proposed methods are more efficient in separating non-Gaussian graph signals.

Fetal heart rate (fHR) evaluation is fundamental to guarantee timely medical intervention in case of pregnancy complications. Due to the limitations of traditional cardiotocography, multichannel electrophysiological recording was proposed as a viable alternative, which requires Blind Source Separation (BSS) techniques. Yet effective and reliable separation of the fetal ECG remains challenging due to multiple noise sources and the effects of varying fetal position. In this work, we demonstrate that the adopted electrode configuration plays a key role in the effectiveness of BSS and propose guidelines for optimal electrode positioning. Moreover, a model is proposed to automatically predict the most suited configuration for accurate BSS-based fHR estimation with a minimal number of leads, to facilitate practical implementation. We compared fHR estimation accuracy with different electrode configurations on in-silico data, identifying the optimal configuration for a recent BSS method. Based on features extracted from raw signals, we proposed a support vector regression model to automatically identify the best electrode configuration in terms of fHR estimation accuracy and to dynamically adjust it to varying fetal presentation. Evaluation was performed on real and synthetic data. Guidelines for the optimal electrode configuration are proposed by using 4 leads. Prediction of configuration quality shows 80.9% accuracy; the optimal configurat- ion is recognized in 92.2% of the subjects. The proposed method successfully predicts the quality of the configurations, demonstrating the impact of the electrode configuration on the BSS performance. The method holds potential for long-term fetal monitoring, by dynamically choosing the optimal configuration.

The indirect method of using a passing vehicle to identify modal properties of a girder bridge has become attractive recently. Compared to the direct method, which requires a lot of sensors installed directly on the bridge itself, the indirect method only requires a single sensor installed on the vehicle to indirectly measure the response of the bridge. However, it is difficult to eliminate the adverse effect of road surface roughness. An indirect approach based on blind source separation is proposed for the first time in this study to identify the bridge element stiffness where two movable vehicles are used. Two identical vehicles stay at rest at the designated measurement points and their vertical accelerations are collected. After one measurement, the two vehicles move to other designated measurement points and the accelerations are collected again. The same procedure is repeated until the two vehicles have moved over all the designated measurement points. Then the blind source separation technique is employed to extract the fundamental mode shape of the bridge and the improved direct stiffness method is adopted to estimate the bridge element stiffness based on the collected data, which are used to monitor the health of the bridge structure and to maintain structure safety and natural symmetry. The proposed method only requires the output response of the vehicle due to the involvement of the blind separation technique. In addition, the proposed method can overcome the adverse effect of road surface roughness because the vehicles only move between two measurements and they stay at rest during one measurement. Numerical simulation was conducted to validate the proposed method, and the effect of various factors such as bridge damping ratio and measurement noise was investigated. Field measurement on Min-Xie bridge in Chongqing city was also carried out to further investigate the feasibility of the proposed method and showed that it can perform well in extracting the fundamental mode shape and evaluating bridge element stiffness.

Blind source separation (BSS) techniques are applied in many domains since they allow separating a set of signals from their observed mixture without the knowledge (or with very little knowledge) of the source signals or the mixing process. Two particular BSS techniques called Second-Order Blind Identification (SOBI) and Blind Modal Identification (BMID) are considered in this paper for the purpose of structural damage detection or fault diagnosis in mechanical systems. As shown on experimental examples, the BMID method reveals significant advantages. In addition, it is demonstrated that damage detection results may be improved significantly with the help of the block Hankel matrix. The main advantage in this case is that damage detection still remains possible when the number of available sensors is small or even reduced to one. Damage detection is achieved by comparing the subspaces between the reference (healthy) state and a current state through the concept of subspace angle. The efficiency of the methods is illustrated using experimental data.

The extraction of the fetal electrocardiogram (FECG) from maternal cutaneous electrode recordings accepts a blind source separation (BSS) formulation. From this perspective, the problem reduces to the estimation of the independent sources of fetal cardiac bioelectric activity. In this contribution, a BSS method based on higher-order statistics is contrasted with a significant classical technique for FECG extraction, such as Widrow's multi-reference adaptive noise cancellation. As a best-case scenario, optimal Wiener-Hopf filtering solutions are considered for this latter method. Both procedures are applied to real multi-channel ECG recordings obtained from a pregnant woman. The experimental outcome demonstrates the more robust performance of the blind technique in this important biomedical application.