Blind separation of convolutive mixtures using joint block diagonalization

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This letter addresses the problem of the nonunitary joint block diagonalization of a given set of complex matrices whose potential applications stem from the blind separation of convolutive mixtures of sources and from the array processing. The proposed algorithm is based on the algebraic optimization of a least-mean-square criterion. One of its advantage is that a pre-whitening stage is no more compulsorily required when this algorithm is applied in the blind source separation context. Computer simulations are provided in order to illustrate its behavior in three cases: when exact block-diagonal matrices are built, then when they are progressively perturbed by an additive Gaussian noise and, finally, in the context of blind separation of convolutive mixtures of temporally correlated sources with estimated correlation matrices. A comparison with a classical orthogonal joint block diagonalization algorithm is also performed, and a new performance index is introduced to measure the performance of the separation. </para>

Second order blind identification (SOBI) technique is a promising independent component analysis (ICA) method to extract somatosensory evoked potential (SEP). This simulation study focused on SEP extraction from EEG and power-line noise contaminated SEP signals at signal to noise ratio (SNR) of -10dB and -20dB. The correlation coefficients between template SEP and SOBI extracted SEP showed significant high similarity (r>0.76) at -10dB and mild acceptable similarity (r>0.6) at -20dB EEG contaminated SEP. However, SOBI extracted SEP showed good performance in power-line noise situation to achieve high correlation coefficients with template SEP (r=0.96). The fast extracted SEP showed stable amplitude and latency, which are almost identical with the SEP template. The results suggested that SOBI is an appropriate method to extract SEP from noisy background.

A new output only modal analysis method is developed in this paper. This method uses continuous wavelet transform to modify a popular blind source separation algorithm, second order blind identification (SOBI). The wavelet modified SOBI (WMSOBI) method replaces original time domain signal with selected time-frequency domain wavelet coefficients, which overcomes the shortcomings of SOBI. Both numerical and experimental studies on bridge models are carried out when there are limited number of sensors. Identified modal properties from WMSOBI are analyzed and compared with fast Fourier transform (FFT), SOBI and eigensystem realization algorithm (ERA). The comparison shows WMSOBI can identify as many results as FFT and ERA. Further case study of structural health monitoring (SHM) on an arch bridge verifies the capability to detect damages by combining WMSOBI with incomplete flexibility difference method.

This paper focuses on the blind source separation of convolutive mixtures based on high order cumulants. It is proved that the zero-forcing of pairwise cross-cumulants of the outputs of separation system is a sufficient criterion for the separation of convolutive mixtures. New algorithm is developed based on this criterion. Simulation results are presented to support the validity of the algorithm.

The modal identification framework known as Blind Modal Identification (BMID) has recently been developed, drawing on techniques from Blind Source Separation (BSS). Therein, a BSS algorithm known as Second Order Blind Identification (SOBI) was adapted to solve the Modal IDentification (MID) problem. One of the drawbacks of the technique is that the number of modes identified must be less than the number of sensors used to measure the vibration of the equipment or structure. In this paper, an extension of the BMID method is presented for the underdetermined case, where the number of sensors is less than the number of modes to be identified. The analytic signal formed from measured vibration data is formed and the Second Order Blind Identification of Underdetermined Mixtures (SOBIUM) algorithm is applied to estimate the complex-valued modes and modal response autocorrelation functions. The natural frequencies and modal damping ratios are then estimated from the corresponding modal auto spectral density functions using a simple Single Degree Of Freedom (SDOF), frequency-domain method. Theoretical limitations on the number of modes identified given the number of sensors are provided. The method is demonstrated using a simulated six DOF mass-spring-dashpot system excited by white noise, where displacement at four of the six DOF is measured. All six modes are successfully identified using data from only four sensors. The method is also applied to a more realistic simulation of ambient building vibration. Seven modes in the bandwidth of interest are successfully identified using acceleration data from only five DOF. In both examples, the identified modal parameters (natural frequencies, mode shapes, modal damping ratios) are compared to the analytical parameters and are demonstrated to be of good quality.

Wind power presents undesirable intermittencies due to the considerable variations in the wind speed which may affect adversely the smooth operation of the grid. Effective wind forecast is essential in order to report the amount of energy supply with high accuracy, which is crucial for planning energy resources for power system operators. In this paper a new statistical method is presented based on independent component analysis (ICA) and autoregressive (AR) model. ICA is utilized in order to exploit the hidden factors which may exist in the wind speed time-series. ICA methods based on exploiting the time structure like second order blind identification (SOBI) can be used as a preliminary step in wind speed forecasting.

An adaptive blind source separation algorithm for the separation of convolutive mixtures of cyclostationary signals is proposed. The algorithm is derived by applying natural gradient iterative learning to a novel cost function which is defined according to the wide sense cyclostationarity of signals and can be deemed as a new member of the family of natural gradient algorithms for convolutive mixtures. A method based on estimating the cycle frequencies required for practical implementation of the proposed algorithm is presented. The efficiency of the algorithm is supported by simulations, which show that the proposed algorithm has improved performance for the separation of convolved cyclostationary signals in terms of convergence speed and waveform similarity measurement, as compared to the conventional natural gradient algorithm for convolutive mixtures. Copyright © 2004 John Wiley &amp; Sons, Ltd.

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.

This article addresses the problem of the Non Unitary Joint Block Diagonalization ( $$\mathsf {NU-JBD}$$ ) of a given set of complex matrices for the blind separation of convolutive mixtures of sources. We propose new different iterative optimization schemes based on Conjugate Gradient, Preconditioned Conjugate Gradient, Levenberg–Marquardt and Quasi-Newton methods. We perform also a study to determine which of these algorithms offer the best compromise between efficiency and convergence speed in the studied context. To be able to derive all these algorithms, a preconditioner has to be computed which requires either the calculation of the complex Hessian matrices or the use of an approximation to these Hessian matrices. Furthermore, the optimal stepsize is also computed algebraically to speed up the convergence of these algorithms. Computer simulations are provided in order to illustrate the behavior of the different algorithms in various contexts: when exactly block-diagonal matrices are considered but also when these matrices are progressively perturbed by an additive Gaussian noise. Finally, it is shown that these algorithms enable solving the blind separation of the convolutive mixtures of sources problem.

Blind source separation for convolutive mixtures based on the joint diagonalization of power spectral density matrices

The paper presents an approach able to separate the vibrations induced by underground traffic from the vibrations induced by other sources, based on second order blind identification (SOBI) algorithm. The signals recorded in different locations of an instrumented building are mixed signals from different internal and external vibration sources. The blind source separation algorithm will estimate the independent vibration sources, as well as the mixing model of them. This model can be used to determine the contribution of each source in different measurement points, to evaluate the effect of vibration sources and their potential for building damage. The approach has been tested in simulation and on a building subject to different traffic forms.

A robust method for removal of artifacts such as eye blinks and electrocardiogram (ECG) from the electroencephalograms (EEGs) has been developed in this paper. The proposed hybrid method fuses support vector machines (SVMs) based classification and blind source separation (BSS) based on independent component analysis (ICA). The carefully chosen features for the classifier mainly represent the data higher order statistics. We use the second order blind identification (SOBI) algorithm to separate the EEG into statistically independent sources and SVMs to identify the artifact components and thereby to remove such signals. The remaining independent components are remixed to reproduce the artifact free EEGs. Objective and subjective results from the simulation studies show that the algorithm outperforms previously proposed algorithms

Blind Source Separation (BSS) is an inverse solution problem based on Second Order Statistic (SOS) and Higher Order Statistic (HOS), with significant applications in the area of acoustics, telecommunications, and biomedicine. In this work, one algorithm based on SOS called Second Order Blind Identification (SOBI), and two HOS algorithms, max-kurtosis, and fastICA was compared using mixed of known signals as sinusoidal, and audio waveforms in order to compare the performance of algorithms using one referenced metric between original and recovered signals, as well as five EEG nearby channels located in a specifical regions on the scalp. The results suggest that fastICA algorithm based on negentropy is performed better in most cases, however, in EEG signals, it is not possible to conclude the same due to the lack of ground truth, therefore, the choice of better ICA algorithm to separate EEG signals it is still an open problem in the biomedical applications.

peer reviewed

The motivating vision behind Sandia's MENTOR/PAL LDRD project has been that of systems which use real-time psychophysiological data to support and enhance human performance, both individually and of groups. Relevant and significant psychophysiological data being a necessary prerequisite to such systems, this LDRD has focused on identifying and refining such signals. The project has focused in particular on EEG (electroencephalogram) data as a promising candidate signal because it (potentially) provides a broad window on brain activity with relatively low cost and logistical constraints. We report here on two analyses performed on EEG data collected in this project using the SOBI (Second Order Blind Identification) algorithm to identify two independent sources of brain activity: one in the frontal lobe and one in the occipital. The first study looks at directional influences between the two components, while the second study looks at inferring gender based upon the frontal component.