Sequential blind source separation based exclusively on second-order statistics developed for a class of periodic signals

An adaptive semiblind signal separation algorithm for the separation of a class of arbitrarily distributed but temporally correlated source signals is introduced in this paper. The proposed adaptive algorithm is based only on second-order statistical(SOS) information and exploits the assumption that the source signals are not strictly spatial statistically independent, and temporal do not identical distributed too. Furthermore, the novel adaptive batch blind signal separation(BSS) method give an adaptive algorithm for correlated source signals. In order to get the ideal separation, the source signals must have different power spectra shapes. Simulation results for real image recordings show that the proposed algorithm has the ability to restore source signals, and its performance is comparable to that of the BSS algorithm such as AMUSE and JADE algorithm. The proposed algorithm is also shown to alleviate the limitation that the classic independent component analysis(ICA) algorithm can separate at most one Gaussian distributed source.

In the context of relating specific brain functions to specific brain structures, second-order blind identification (SOBI) is one of the blind source separation algorithms that have been validated extensively in the data domain of human high-density EEG. Here we provide a review of empirical data that (1) validate the claim that SOBI is capable of separating correlated neuronal sources from each other and from typical noise sources present during an EEG experiment; (2) demonstrating the range of experimental conditions under which SOBI is able to recover functionally and neuroanatomically meaningful sources; (3) demonstrating cross- as well as within-subjects (cross-time) reliability of SOBI-recovered sources; (4) demonstrating efficiency of SOBI separation of neuronal sources. We conclude that SOBI may offer neuroscientists as well as clinicians a cost-effective way to image the dynamics of brain activity in terms of signals originating from specific brain regions using the widely available EEG recording technique.KeywordsBSSICASOBISource modelingSource localizationSingle-trial analysishuman EEGMultichannel

Blind single-channel source separation is a long-standing machine learning and signal processing problem. Traditional blind source separation (BSS) algorithms were proposed to solve this task utilizing multiple signal constraints. Generative adversarial network (GAN) are free from statistical constraints and samples, but the role of adversarial training in the task of BSS has not been fully demonstrated. Therefore, a new separation network model that enables to learn the known separated signal distribution from the stepwise fine estimation of the unknown mixture distribution was presented in this paper, and a self-attention mechanism was introduced to solve the problem of the blurring details of the generated image by the generator which preserves image details in the process of image separation. Compared with the existing single-channel blind source separation algorithm based on generative adversarial network-neural egg separation (NES), the detailed information of this new separation algorithm is more prominent, and the source signal in the mixed image has been separated more effectively, and has better separation performance than the classic blind source separation algorithms.

Advances in Bayesian computational technology in the last decade have enabled the development of new source separation and source localization algorithms. These algorithms are greatly improved by the encoding of prior information about a specific problem in the form of the chosen relevant model parameters, the assignment of the likelihood functions, and the assignment of the prior probabilities of the model parameter values. I refer to such source separation algorithms as informed source separation for the reason that they are endowed with specific and often vital information about the problem. Furthermore, the Bayesian methodology allows source separation to be united with source localization simply by including the model parameters that are of interest to the researcher. Here, I will discuss the union of source separation and source localization under the Bayesian methodology, the incorporation of prior information, and the construction of an informed algorithm using the new computational technologies that allow us to estimate the values of the parameters that define these high‐dimensional problems.

The second-order blind identification (SOBI) algorithm (Belouchrani et al., 1997) is a classical blind source separation (BSS) algorithm for stationary sources. The weights-adjusted SOBI (WASOBI) algorithm (Yeredor 2000) proposed a reformulation of the SOBI algorithm as a weighted nonlinear least squares problem, and showed how to obtain asymptotically optimal weights, under the assumption of Gaussian Moving Average (MA) sources. In this paper, we extend the framework by showing how to obtain the (asymptotically) optimal weight matrix also for the cases of auto-regressive (AR) or ARMA Gaussian sources (of unknown parameters), bypassing the apparent need for estimation of infinitely many correlation matrices. Comparison with other algorithms, with the Cramér Rao bound and with the analytically predicted performance is presented using simulations. In particular, we show that the optimal performance can be attained with fewer estimated correlation matrices than in the Gaussian Mutual Information approach (which is also optimal in this context).KeywordsCorrelation MatriceBlind Source SeparationGaussian SourceBlind SeparationObservation LengthThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In the recent past, blind source separation (BSS) algorithms using multivariate statistical data analysis technique have been successfully used for source identification and separation in the field of biomedical and statistical signal processing. Recently numbers of different BSS techniques have been developed. With BSS methods being the feasible method for source separation and decomposition of biosignals, it is important to compare the different techniques and determine the most suitable method for the applications. This paper presents the performance of five BSS algorithms (SOBI, TDSEP, FastICA, JADE and Infomax) for decomposition of sEMG to identify subtle finger movements. It is observed that BSS algorithms based on second-order statistics (SOBI and TDSEP) gives better performance compared to algorithms based on higher-order statistics (FastICA, JADE and infomax).

A novel blind separation approach using higher-order time-frequency distributions is presented. The concept of higher-order time-frequency distribution matrix is also introduced. It is devised to primarily separate sources with temporal nonstationary signal characteristics. So far, this problem has been solved using statistical information available on the source signals. In contrast to well known blind source separation approaches using second-order statistics (SOS) and/or higher-order statistics (HOS) which rely on stationarity properties of the signals, the proposed approach allows separation of the sources with nonstationarity properties. In addition, the effect of spreading the noise power while localizing of the source energy in the time-frequency domain amounts to increasing the signal to noise ratio. A computationally feasible implementation is presented based on joint diagonalization of the matrices of the principal slices of the time-multifrequency domain of support of the cumulant-based Wigner trispectrums. Numerical examples demonstrate the effectiveness of the proposed approach.

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.

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 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.

Most of the existing algorithms for blind sources separation have a limitation that sources are statistically independent. However, in many practical applications, the source signals are nonnegative and mutual statistically dependent signals. When the observations are nonnegative linear combinations of nonnegative sources, the correlation coefficients of the observations are larger than these of source signals. In this letter, a novel Nonnegative Matrix Factorization (NMF) algorithm with least correlated component constraints to blind separation of convolutive mixed sources is proposed. The algorithm relaxes the source independence assumption and has low-complexity algebraic computations. Simulation results on blind source separation including real face image data indicate that the sources can be successfully recovered with the algorithm.

A frequently encountered problem in signal processing is harmonic retrieval in additive colored Gaussian or non-Gaussian noise, especially when the frequencies of the harmonic signals are very close in space. The purpose of this paper is to develop an efficient Blind Source Separation (BSS) algorithm from linear mixtures of source signals, which enables to separate harmonic source signals using only one observed channel signal even if the frequencies of the harmonic signals are closely spaced. First, we establish the BSS based harmonic retrieval model in additive noise by using the only one observed channel, and analyze the fundamental principle by utilizing BSS method to retrieve harmonics. Then, we propose a BSS-based approach to the harmonic retrieval by resorting the concept of W-disjoint orthogonality in the over-complete BSS situation, and as a result, we get the separation algorithm using only one channel mixed signals. Simulation results show that the proposed separation algorithm-BSS-HR is able to separate the harmonic source signals.

We present a simple efficient local unsupervised learning algorithm for online adaptive multichannel blind deconvolution and separation of i.i.d. sources. Under mild conditions, there exits a stable inverse system so that the source signals can be exactly recovered from their convolutive mixtures. Based on the existence of the inverse filter, we construct a two-stage neural network which consists of blind equalization and source separation. In the blind equalization stage, we employ anti-Hebbian learning in the temporal domain for decorrelation. For blind separation, we can apply any existing algorithms. Extensive computer simulations confirm the validity and high performance of our proposed learning algorithm.

The paper proposes a new BSS algorithm based on the second-order statistics. By jointly diagonalizing the time delay correlation matrix of the observed signals and using the improved new non-orthogonal joint diagonalization (NOJD) method, a better solution is achieved. The proposed algorithm can successfully separate communication signals under SNR as low as 10dB and the over-determined mode regardless of the signals’ modulation methods. Signal to Interference Noise Ratio (SINR) is used to prove the superiority of the proposed algorithm over the classical Second-Order Blind Identification (SOBI).

For blind source separation algorithm separation accuracy is not high question, this paper proposes a joint algorithm that combining joint approximative diagonalization of eigenmatrix algorithm (JADE) with second-order blind identification (SOBI) algorithm together. At the same time, this paper applies cyclic cumulant to the joint algotithm which takes advantage of cyclic cumulant's suppress noise characteristics. Then this paper proposes a joint algorithm basing on cyclostationarity optimization. The simulation results show that the algorithm can realize effective extraction of the desired signal, higher separation performance, and higher convergence speed.