Linear Instantaneous Mixtures Research Articles

Blind single-channel lamb wave mode separation using independent component analysis on time-frequency signal representation

Guided waves are widely employed in non-destructive testing, but the presence of dispersion and multiple modes poses a challenge in detecting and separating the received signals, thereby affecting the performance of testing algorithms. Traditional methods for ultrasonic wave mode separation rely on time-frequency transforms, which often require extensive post-processing or the selection of specific frequency points for mode separation. In contrast, this paper introduces a blind separation method that utilizes independent component analysis to facilitate blind single-channel Lamb wave multimode separation. The proposed method demonstrates robust performance even under high noise power levels, while effectively localizing the source energy in the time-frequency domain. Numerical and experimental tests validate the effectiveness of the proposed method, showcasing its ability to successfully separate signals from instantaneous linear mixtures.

An adaptive single channel EMD-TNMF blind source separation algorithm for both instantaneous and convolutive mixed signal

Single channel blind source separation (SCBSS) using time-frequency nonnegative matrix factorization (NMF) has some shortcomings, where the source number and convolution order must be known and it’s sensitive to the factors (e.g. window function, window length and overlap ratio of adjacent windows). To compensate these shortcomings that cannot meet the real application, we proposed an adaptive EMD-TNMF algorithm, which can estimate both the source number and the convolution order and is applicable to both single channel linear instantaneous and convolutive mixtures. Firstly, the single channel signal is mapped into multiple channels by utilizing empirical mode decomposition (EMD), and the number of independent sources is estimated by applying eigenvalue descent ratio of the IMFs’ covariance matrix. Secondly, the autocorrelation-based method is used to estimate the convolution order. Thirdly, the nonnegative matrix is constructed by adding one positive matrix (all elements are positive). Finally, in time domain, NMF algorithm is used to separate source signals. The algorithm’s performance is verified by two experiments where the single channel signal is linear instantaneous mixing of four artificial signals and linear convolutive mixing of two speech signals respectively. Results show that this algorithm can estimate the source number and convolution order correctly and obtain better separated source signals.

A Moment-Based Estimation Strategy for Underdetermined Single-Sensor Blind Source Separation

We investigate the blind identification and separation of underdetermined linear instantaneous mixtures with a single sensor and an arbitrary known number of sources with finite known support and uniform distribution. We propose channel estimators based on the high-order statistics of the received signal and on the rotational symmetries of the source constellations. Explicit expressions for distinct and equal rotation orders are derived. The proposed estimators are used as initializers for the iterative least squares with enumeration algorithm to enhance its convergence properties. Simulation results on several high interference two-user wireless communication scenarios show that our initialization strategy achieves a substantial performance gain compared to other traditional initializers.

Gradient Algorithms for Complex Non-Gaussian Independent Component/Vector Extraction, Question of Convergence

We revise the problem of extracting one independent component from an instantaneous linear mixture of signals. The mixing matrix is parameterized by two vectors, one column of the mixing matrix and one row of the de-mixing matrix. The separation is based on the non-Gaussianity of the source of interest, while the other background signals are assumed to be Gaussian. Three gradient-based estimation algorithms are derived using the maximum likelihood principle and are compared with the Natural Gradient algorithm for Independent Component Analysis and with One-unit FastICA based on negentropy maximization. The ideas and algorithms are also generalized for the extraction of a vector component when the extraction proceeds jointly from a set of instantaneous mixtures. Throughout the paper, we address the problem of the size of the region of convergence for which the algorithms guarantee the extraction of the desired source. We show how that size is influenced by the ratio of powers of the sources within the mixture. Simulations confirm this observation where several algorithms are compared. They show various convergence behavior in a scenario where the source of interest is dominant or weak. Here, our proposed modifications of the gradient methods taking into account the dominance/weakness of the source show improved global convergence property.

Single channel blind source separation on the instantaneous mixed signal of multiple dynamic sources

Abstract Single Channel Blind Source Separation (SCBSS) has had many algorithms for artificial mixed signal, where the number of mixing sources is assumed to be known, and mixed signal used in validation algorithm only contains two signal sources. However, in real-world application, the mixed number of sources is unknown and is usually more than two. This paper presents a new single-channel blind source separation algorithm based on the multi-channel mapping and Independent Component Analysis (ICA), which supposes that mixed signal comes from a dynamic system in which any component depends on the interaction of other components and signals are linear instantaneous mixture. The mathematical model demonstrates the single channel signal of linear instantaneous mixture. In order to map single channel signals into multi-channel signals, Takens theory and C-C method are used to estimate the time delay and the embedding dimension in the time series of the dynamic system. FastICA for multi-channel blind source separation is improved by using FSS-Kernel (Finite Support Samples Kernel), where the nonlinear function of FastICA is replaced by PDF (probability density function) and estimated by FSS-Kernel. The experiments are conducted to evaluate the proposed algorithm of single channel blind source separation, in which the synthetic signals and speech signals are used respectively. The experiment results show that the proposed method is very effective to estimate the number of independent components and is practical to separate two or more mixed signals.

Underdetermined Joint Blind Source Separation of Multiple Datasets

In this paper, we tackle the problem of jointly separating instantaneous linear underdetermined mixtures of latent sources from multiple data sets, where the number of sources exceeds that of observations in each data set. Currently available blind source separation (BSS) methods, including joint BSS (JBSS) and underdetermined BSS (UBSS), cannot address this underdetermined problem effectively. We exploit the second-order statistics of observations, and present a novel BSS method, referred to as underdetermined joint BSS for multiple data sets (UJBSS-m), as a generalization of our previous work on two data sets. In this paper, the cross correlation between each pair of data sets is modeled by a third-order tensor in which a set of spatial covariance matrices corresponding to different time delays are stacked. Considering the latent common structure of these constructed tensors, the mixing matrices are jointly estimated via joint canonical polyadic decomposition of these specialized tensors. Furthermore, we recover the sources from each data set separately based on the estimated mixing matrices. Simulation results demonstrate that the proposed UJBSS-m method yields superior performances when compared with commonly used single-set UBSS and JBSS methods.

Blind source separation for vibration-based diagnostics of rotorcraft bearings

The vibration signals from sensors monitoring the activity of individual bearings in a power train unit may be linear instantaneous mixtures of vibrations generated by various dynamic components. Generally, an exact physical model describing the mixing process and the contribution of each dynamic component to the received sensor signal is not available. Vibration source signals from defective bearings often overlap in time and frequency, and, as such, the direct use of time- and frequency-domain methods may result in erroneous diagnostic information. This paper implements blind source separation (BSS) to demix sensor signals into correctly identifiable vibration source signals without the need of the vibration path property and sensor layout. Experimental vibration data from spalled, corroded, and healthy rotorcraft bearings are used with five representative BSS algorithms. The separation accuracy of these algorithms is then compared using various performance metrics. Results show that despite the inherent statistical dependence and near Gaussianity, it is possible to isolate vibration sources from mixed sensor signals using second- and higher-order statistics of the signals. The paper also identifies the limitations of the BSS technique and provides a remedy and recommendation for its implementation in rotorcraft bearing fault detection.

Nonnegative Mixture for Underdetermined Blind Source Separation Based on a Tensor Algorithm

In this study, a tensor algorithm is proposed to blindly separate an instantaneous linear underdetermined mixture with non-stationary sources and nonnegative mixing matrix. It proceeds in two steps: 1) estimating the mixing matrix and 2) recovering the source signals. First, a canonical tensor model is constructed using a fourth-order cumulant tensor of the observed signals to estimate the mixing matrix. Then, an improved hierarchical alternating least squares algorithm is used to decompose the canonical tensor model, which ensures that all elements of the mixing matrix are positive. Finally, the sources are recovered using a minimum mean-squared error beamformer approach without any hypothetical limitation. We apply two classes of data (speech signals and biomedical signals) to substantiate the effectiveness of the proposed algorithm for underdetermined blind source separation.

A heuristic approach for blind source separation of instant mixtures

In this paper we present a methodology for blind source separation (BSS) based on a coherence function to solve the problem of linear instantaneous mixtures of signals. The proposed methodology consists of minimizing the coherence function using a heuristic algorithm based on the simulating annealing method. Also, we derived an analytical expression of the coherence for the BSS model, in which it is found that independent and identically distributed (iid) Gaussian components can be recovered. Our results show satisfactory performance in comparison with traditional methods.

Quantification of the effects of volume conduction on the EEG/MEG connectivity estimates: an index of sensitivity to brain interactions

In the context of EEG/MEG, the term ‘volume conduction (VC) effects’ refers to the recording of an instantaneous linear mixture of multiple brain source activities by each EEG/MEG channel. VC effects may lead to the detection of spurious functional/effective couplings among EEG/MEG channels that are not caused by brain interactions. It is of importance to determine which detected couplings are indicators of brain interactions and which originate from the VC artefacts. In this paper, a quantitative framework is proposed to explore the origin of detected channel couplings by using two types of surrogate datasets. Also, a sensitivity index (called SI) is proposed to compare the power of different connectivity measures to discriminate between the brain interactions and the instantaneous linear mixing effects. We use seven different functional connectivity estimators to evaluate our method on simulation models and resting state EEG data. The error rate of the proposed framework for simulation data by using each of the connectivity estimators is less than 5.2%. Also, SI ranks these connectivity estimators according to their sensitivity to brain interactions in the presence of VC artefacts. As expected, the connectivity measures which are theoretically robust to VC artefacts yield high SI in simulation models and EEG data. In addition, for EEG data in the alpha frequency band the reproducible functional couplings which are indicators of brain interactions are in the back-front directions. This is consistent with the previous studies in this field.

Audio visual speech source separation via improved context dependent association model

In this paper, we exploit the non-linear relation between a speech source and its associated lip video as a source of extra information to propose an improved audio-visual speech source separation (AVSS) algorithm. The audio-visual association is modeled using a neural associator which estimates the visual lip parameters from a temporal context of acoustic observation frames. We define an objective function based on mean square error (MSE) measure between estimated and target visual parameters. This function is minimized for estimation of the de-mixing vector/filters to separate the relevant source from linear instantaneous or time-domain convolutive mixtures. We have also proposed a hybrid criterion which uses AV coherency together with kurtosis as a non-Gaussianity measure. Experimental results are presented and compared in terms of visually relevant speech detection accuracy and output signal-to-interference ratio (SIR) of source separation. The suggested audio-visual model significantly improves relevant speech classification accuracy compared to existing GMM-based model and the proposed AVSS algorithm improves the speech separation quality compared to reference ICA- and AVSS-based methods.

PARAFAC-Based Blind Identification of Underdetermined Mixtures Using Gaussian Mixture Model

This paper presents a novel algorithm, named GMM-PARAFAC, for blind identification of underdetermined instantaneous linear mixtures. The GMM-PARAFAC algorithm uses Gaussian mixture model (GMM) to model non-Gaussianity of the independent sources. We show that the distribution of the observations can also be modeled by a GMM, and derive a maximum-likelihood function with regard to the mixing matrix by estimating the GMM parameters of the observations via the expectation-maximization algorithm. In order to reduce the computation complexity, the mixing matrix is estimated by maximizing a tight upper bound of the likelihood instead of the log-likelihood itself. The maximum of the tight upper bound is obtained by decomposition of a three-way tensor which is obtained by stacking the covariance matrices of the GMM of the observations. Simulation results validate the superiority of the GMM-PARAFAC algorithm.

Extracting Signals Robust to Electrode Number and Shift for Online Simultaneous and Proportional Myoelectric Control by Factorization Algorithms

Previous research proposed the extraction of myoelectric control signals by linear factorization of multi-channel electromyogram (EMG) recordings from forearm muscles. This paper further analyses the theoretical basis for dimensionality reduction in high-density EMG signals from forearm muscles. Moreover, it shows that the factorization of muscular activation patterns in weights and activation signals by non-negative matrix factorization (NMF) is robust with respect to the channel configuration from where the EMG signals are obtained. High-density surface EMG signals were recorded from the forearm muscles of six individuals. Weights and activation signals extracted offline from 10 channel configurations with varying channel numbers (6, 8, 16, 192 channels) were highly similar. Additionally, the method proved to be robust against electrode shifts in both transversal and longitudinal direction with respect to the muscle fibers. In a second experiment, six subjects directly used the activation signals extracted from high-density EMG for online goal-directed control tasks involving simultaneous and proportional control of two degrees-of-freedom of the wrist. The synergy weights for this control task were extracted from a reference configuration and activation signals were calculated online from the reference configuration as well as from the two shifted configurations, simulating electrode shift. Despite the electrode shift, the task completion rate, task completion time, and execution efficiency were generally not statistically different among electrode configurations. Online performances were also mostly similar when using either 6, 8, or 16 EMG channels. The robustness of the method to the number and location of channels, proved both offline and online, indicates that EMG signals recorded from forearm muscles can be approximated as linear instantaneous mixtures of activation signals and justifies the use of linear factorization algorithms for extracting, in a minimally supervised way, control signals for simultaneous multi-degree of freedom prosthesis control.

Independent component analysis based on first-order statistics

This communication puts forward a novel method for independent source extraction in instantaneous linear mixtures. The method is based on the conditional mean of the whitened observations and requires some prior knowledge of the positive support of the desired source. A theoretical performance analysis yields the closed-form expression of the asymptotic interference-to-signal ratio achieved by this technique. The analysis includes the effects of inaccuracies in the estimation of the positive support of the desired source in single-step and iterative implementations of the algorithm. Numerical experiments validate the fitness of the asymptotic approximations. As it is based on first-order statistics, the method is extremely cost-effective, which makes it an attractive alternative to second- and higher-order statistical techniques in power-limited scenarios.

Informed Source Separation of Linear Instantaneous Under-Determined Audio Mixtures by Source Index Embedding

In this paper, we address the issue of underdetermined source separation of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> nonstationary audio sources from a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> -channel linear instantaneous mixture ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <; <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> ). This problem is addressed with a specific coder-decoder configuration. At the coder, source signals are assumed to be available before the mixing is processed. A time-frequency (TF) joint analysis of each source signal and mixture signal enables to select the subset of sources (among <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> ) leading to the best separation results in each TF region. A corresponding source(s) index code is imperceptibly embedded into the mix signal using a watermarking technique. At the decoder, where the original source signals are unknown, the extraction of the watermark enables to invert the mixture in each TF region to recover the source signals. With such an informed approach, it is shown that five instruments and singing voice signals can be efficiently separated from two-channel stereo mixtures, with a quality that significantly overcomes the quality obtained by a semi-blind reference method and enables separate manipulation of the source signals during stereo music restitution (i.e., remixing).

Extracting post-nonlinear signal with reference

Constrained independent component analysis (cICA) is an important technique which can extract the desired sources from the mixtures. The post-nonlinear (PNL) mixture model is more realistic and accurate than the linear instantaneous mixture model in many practical situations. In this paper, we address the problem of extracting the desired source as the first output from the PNL mixture. The prior knowledge about the desired source, such as its rough template (reference), is assumed to be available. Two approaches of extracting PNL signal with reference are discussed. Then a novel algorithm which alternately optimizes the contrast function and the closeness measure between the estimated output and the reference signal is proposed. The inverse of the unknown nonlinear function in the PNL mixture model is approximated by the multi-layer perception (MLP) network. The correctness and validity of the proposed algorithm are demonstrated by our experiment results.

A Novel Noise Elimination Method for MEMS Sensor

It is inevitable that measured signals are contaminated with noise when MEMS sensor is used for an outdoor measurement. So the obtained signals need noise elimination, which is one of key technologies for signal conditioning. In this paper, a novel noise elimination method based on algorithm of blind source separation (BSS) for MEMS sensor is proposed to separate the source signals from the mixed signals with noises. The BSS algorithm based on maximum signal noise ratio (SNR) is a method of global optimal property, using the characteristic that SNR is maximal when statistically independent source signals are completely separated.The algorithm has a low computational complexity for instantaneous linear mixture signals. It is effective to acquire the source signals from the mixed signals with noises obtained by MEMS sensor,and is successfully verified by simulation experiment of BSS algorithm.The result of noise elimination experiment has achieved signal conditioning and eliminates ambient noises for MEMS sensor signals.

Weight Adjusted Tensor Method for Blind Separation of Underdetermined Mixtures of Nonstationary Sources

In this paper, a novel algorithm to blindly separate an instantaneous linear underdetermined mixture of nonstationary sources is proposed. It means that the number of sources exceeds the number of channels of the available data. The separation is based on the working assumption that the sources are piecewise stationary with a different variance in each block. It proceeds in two steps: 1) estimating the mixing matrix, and 2) computing the optimum beamformer in each block to maximize the signal-to-interference ratio of each separated signal with respect to the remaining signals. Estimating the mixing matrix is accomplished through a specialized tensor decomposition of the set of sample covariance matrices of the received mixture in each block. It utilizes optimum weighting, which allows statistically efficient (CRB attaining) estimation provided that the data obey the assumed Gaussian piecewise stationary model. In simulations, performance of the algorithm is successfully tested on blind separation of 16 speech signals from nine linear instantaneous mixtures of these signals.

Anechoic Blind Source Separation Using Wigner Marginals

Blind source separation problems emerge in many applications, where signals can be modeled as superpositions of multiple sources. Many popular applications of blind source separation are based on linear instantaneous mixture models. If specific invariance properties are known about the sources, for example, translation or rotation invariance, the simple linear model can be extended by inclusion of the corresponding transformations. When the sources are invariant against translations (spatial displacements or time shifts) the resulting model is called an anechoic mixing model. We present a new algorithmic framework for the solution of anechoic problems in arbitrary dimensions. This framework is derived from stochastic time-frequency analysis in general, and the marginal properties of the Wigner-Ville spectrum in particular. The method reduces the general anechoic problem to a set of anechoic problems with non-negativity constraints and a phase retrieval problem. The first type of subproblem can be solved by existing algorithms, for example by an appropriate modification of non-negative matrix factorization (NMF). The second subproblem is solved by established phase retrieval methods. We discuss and compare implementations of this new algorithmic framework for several example problems with synthetic and real-world data, including music streams, natural 2D images, human motion trajectories and two-dimensional shapes.

Performance–lifetime tradeoff for source extraction in multihop sensor networks

AbstractThis paper intends to reveal the performance–lifetime tradeoff for source extraction in a multihop sensor network. The randomly deployed sensor network consists of multiple independent branches. The leaf node in each branch takes an observation from the sensing field. The observation is assumed to be a noisy instantaneous linear mixture of the sources. To account for the bandwidth constraint, each leaf node quantizes its observation and sends the quantized data to the sink in a multihop fashion. The observed mixtures are reconstructed at the sink and are utilized to extract the sources. The accumulated bit error probability in each branch depends on the number of hops and the bit error probability of each channel in that branch. The communication errors affect the accuracy of reconstructing mixtures, and hence affect the performance of source extraction. Network lifetime is defined and analyzed under both per‐sensor energy constraint and network energy constraint. The tradeoff between performance and network lifetime is described by optimization problems and the conditions for optimization are identified. As a by‐product, the conditions for maximizing the network lifetime are also identified. Simulation results demonstrate that the tradeoff exists under certain situations. Copyright © 2010 John Wiley &amp; Sons, Ltd.