Bayesian blind source separation for brain imaging

In the case of multiple nonstationary independent source signals and linear instantaneous time-varying mixing systems, it is difficult to adaptively separate the multiple source signals. Therefore, the adaptive blind source separation (BSS) problem is firstly formally expressed and compared with tradition BSS problem. Then, we propose an adaptive blind identification and separation method based on the variable learning rate equivariant adaptive source separation via independence (EASI) algorithm. Furthermore, we analyze the scope and conditions of variable-learning rate EASI algorithm. The adaptive BSS simulation results also show that the variable learning rate EASI algorithm provides better separation effect than the fixed learning rate EASI and recursive least-squares algorithms.

A robust H∞ learning approach to blind separation of slowly time-varying mixture of acoustic electromechanical signals

This paper studies the problem of blind source separation (BSS) under the assumption that the source signals are cyclostationary. Attention is restricted to methods based on second-order cyclostationary statistics (SOCS). Necessary and sufficient conditions for SOCS-based identifiability and SOCS-based separability are presented. Algorithms are developed to achieve BSS using only SOCS.

We address the problem of blind source separation of non-stationary signals of which only instantaneous linear mixtures are observed. A blind source separation approach exploiting both auto-terms and cross-terms of the time-frequency (TF) distributions of the sources is considered. The approach is based on the simultaneous diagonalization and anti-diagonalization of spatial TF distribution matrices made up of, respectively, auto-terms and cross-terms. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach and compare its performances with existing TF-based methods.

Combining the advantages of local mean decomposition and variational Bayesian hidden Markov model, a blind source separation method for mechanical faults based on local mean decomposition and variational Bayesian hidden Markov model is proposed. In the proposed method, the non-stationary signals are decomposed into a series of production functions by the local mean decomposition, then the obtained production functions and the original observed signals are used to construct new observation signals, therefore the underdetermined blind source separation problem is transformed into the overdetermined blind source separation problem. Finally, the source signals are estimated by the variational Bayesian hidden Markov model method. The proposed method has been successfully applied to the blind separation of bearing faults, and the experiment results verify the effectiveness of the proposed method. The obtained outcome in this paper provides an effective separation method for mechanical fault diagnosis.

The problem of blind source separation (BSS) for multiple-input multiple-output (MIMO) autoregressive (AR) mixtures is addressed in this paper. A new time-domain method for system identification and BSS is proposed based on the Gaussian mixture model (GMM) for sources distribution. The algorithm is based on the generalized expectation-maximization (GEM) method for joint estimation of the AR model parameters and the GMM parameters of the sources. The method is tested via simulations of synthetic and real audio signals. The results show that the proposed algorithm outperforms the well-known multidimensional linear predictive coding (LPC), and it achieves higher signal-to-interference ratio (SIR) in the BSS problem.

This paper deals with the problem of blind source separation which consists of recovering a set of signals from instantaneous linear mixture of them. So far, this problem has been solved using statistical information available on the source signals. Here, we propose an approach for blind source separation based on time-frequency (t-f) signal representations. This approach is based on a `joint diagonalization' of a combined set of time frequency distribution matrices which correspond to different t-f points. It relies on the difference in the t-f signatures of the sources to be separated. In contrast to existing techniques, the proposed approach allows the separation of Gaussian sources with identical spectra shape. Because of changes incurred in the t-f signal structures due to time- delay, the new approach can be employed to separate multipath signals received by multi-sensor array. Moreover, the effects of spreading the noise power while localizing the source energy in the time frequency domain amounts to increasing the signal to noise ratio and hence improved performance. Numerical examples are provided to illustrate the effectiveness of our method.

The problem of blind source separation (BSS) has been intensively studied by the signal processing community. The first solutions to deal with BSS were proposed in the 1980's and are founded on the concept of independent component analysis (ICA). More recently, aiming at tackling some limitations of ICA-based methods, much attention has been paid to alternative BSS approaches. In this tutorial, in addition to providing a brief review of the classical BSS framework, we present two research trends in this area, namely source separation over Galois fields and sparse component analysis. For both subjects, we provide an overview of the main criteria, highlighting scenarios that can benefit from these more recent BSS paradigms.

The problem of sparse Blind Source Separation (BSS) has been extensively studied when the noise is additive and Gaussian. This is however not the case when the measurements follow Poisson or shot noise statistics, which is customary with counting-based measurements. To that purpose, we introduce a novel sparse BSS algorithm coined pGMCA (poisson-Generalized Morphological Component Analysis) that specifically tackles the blind separation of sparse sources from measurements following Poisson statistics. The proposed algorithm builds upon Nesterov's smoothing technique to define a smooth approximation of sparse BSS, with a data fidelity term derived from the Poisson likelihood. This allows to design a block coordinate descent-based minimization procedure with a simple choice of the regularization parameter. Numerical experiments have been carried out that illustrate the robustness of the proposed method with respect to Poisson noise. The pGMCA algorithm has been further evaluated in a realistic astrophysical X-ray imaging setting.

The aim of this paper is to solve the blind source separation (BSS) problem using the temporal independent component analysis (ICA) model. In contrast to ordinary ICA, except for independent assumption, the temporal structure of the source components is taken into account. After combing the virtues of both high order statistics and the temporal second-order information of the source signals, we can get the novel strengthened BSS algorithm-STICA algorithm by using the joint approximate diagonalisation of eigen-matrices (JADE) method. The proposed STICA can not only separate the spatial independent random variables but also the spatial independent time series or both of them exist simultaneously, especially when the sources have non-symmetric distributed time series.

In this paper, we propose a novel algorithm for underdetermined blind identification problem in blind source separation. The proposed algorithm is based on the charrelation matrix of observed signals. The charrelation matrix not only can be considered as a generalized second-order covariance matrix, but also incorporates higher-order information. It is significant for blind separation problem based on statistic characteristics to extract statistical information. The problem of underdetermined blind identification is converted as a tensor decomposition model. The mixing matrix can be estimated from the rank-1 terms of the tensor decomposition. Theoretical analysis and simulation results illustrate the proposed algorithm performs competitive estimation performance compared to the underdetermined blind identification algorithm based on second-order covariance and fourth-order cumulant.

An improvement in the multimodal approach to the problem of blind source separation (BSS) of moving sources is proposed. The challenge of BSS for moving sources is that the mixing filters are time varying. Thus the unmixing filters should also be time varying, which are difficult to calculate from only statistical information avail able from limited number of audio samples. Therefore, in the pro posed approach a robust least square frequency invariant data independent (RLSFIDI) beamformer is implemented to perform real time speech enhancement and provide separation of the moving sources. Direction of arrival information of the sources is obtained from the visual 3-D tracker based on a Markov Chain Monte Carlo particle filter (MCMC-PF). The uncertainties in source localization and direction of arrival information are controlled by using convex optimization approach in the beamformer design. This provides robust ness with a wider main lobe for source of interest (SOI) and wider attenuation pattern to block the interference. In addition, white noise gain (WNG) constraint is used to control the beamformer sensitivity. Experimental results show that by utilizing RLSFIDI beamformer a significant improvement in BSS performance for moving sources is achieved in a low reverberant environment.

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.

A new method for solving the permutation problem in the frequency-domain Blind Source Separation(BSS) was presented.This new method divided the whole frequency-domain into three sections and applied different permutation algorithms to different sections.The neighboring frequency correlation and harmonic frequency correlation coefficient of signal amplitudes were used together for the low-frequency section,the direction of arrival estimation for speech sources for the mid-frequency section,and the combination of correlation coefficient comparison and direction estimation for the high-frequency section,respectively.Experimental results show that the new method provides a more robust and precise solution to the permutation problem than the algorithm only with interfrequency correlation coefficient of signal amplitudes or only with direction of arrival estimation for sources.

ERP is commonly obtained by averaging over segmented EEC epochs. In case artifacts are present in the raw EEC measurement, pre-processing is required to prevent the averaged ERP waveform being interfered by artifacts. The simplest pre-processing approach is by rejecting trials in which presence of artifact is detected. Alternatively artifact correction instead of rejection can be performed by blind source separation, so that waste of ERP trials is avoided. In this paper, we propose a second order statistics based blind source separation approach to ERP artifact correction. Comparing with blind separation using independent component analysis, second order statistics based method does not rely on higher order statistics or signal entropy, and therefore leads to more robust separation even if only short epochs are available.