Fast Adaptive BSS Algorithm for Independent/Dependent Sources

Blind source separation (BSS) consists in processing a set of observed mixed signals to separate them into a set of original components. Most of the current blind separation methods assumes that the source signals are “as statistically independent as possible” given the observed data. In many real-world situations, however, this hypothesis does not hold. In order to cope with such signals, a first geometric method was proposed that separates statistically dependent signals, provided that they are nonnegative and locally orthogonal.This paper presents a new geometric method for the separation of nonnegative source signals which relies on a working assumption that is weaker than local orthogonality. The separation problem is expressed as the identification of relevant facets of the data cone. After a rigorous proof of the proposed method, the details of the separation algorithm are given. Experiments on signals from various origins clearly show the efficiency of the new procedure.

Blind extraction or separation statistically independent source signals from their linear mixtures have been well studied in the last two decades, which is realised by searching for local extrema of certain objective functions. In this paper, by employing nonparametric non-Gaussianity (NG) measure, a blind source separation/extraction (BSS/BSE) algorithm is derived to separate or extract statistically dependent source signals from their underdetermined or determined linear mixtures. Firstly, we show that maximisation NG measure can separate/extract statistically weak dependent source signals. Then, the nonparametric NG measure is defined by statistical distances between different cumulative distribution function (CDF) of separated signals, which can be estimated by quantiles and order statistics (OS) using L2 norm efficiently. Finally, the nonparametric NG measure aided algorithm is optimised by a deflation procedure. Simulation results for synthesis and real world data show that the proposed algorithm can extract the desired dependent source signals and yield expected performance.

Blind Signal Separation II. Linear, Convolutive Combinations: II. Linear, Convolutive Combinations

We propose an independent component analysis (ICA) algorithm which can separate mixtures of sub- and super- Gaussian source signals with self-adaptive nonlinearities. The ICA algorithem in the framework of natural Riemannian gradient is derived using the parameterized Weibull density model. The nonlinear function in ICA algorithem is self-adaptive and is controlled by the shape parameter of Weibull density model. Computer simulation results confirm the validity and high performance of the proposed algorithm Key words: Independent component analysis, weibull distribution, maximum likelihood, sub- and super- Gaussian, blind signal separation.

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.

Blind separation of non-stationary sources using continuous density hidden Markov models

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.

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.

Suppressive interference is a common interference signal for synthetic aperture radar (SAR) that can seriously affect the target identification and imaging results of SAR. This paper proposes a method for suppressing suppressive jamming using blind source separation (BSS) for singular value and eigenvalue decomposition based on information entropy. First, we developed an airborne SAR imaging geometry model and a suppressive interference signal mixing model. Next, we perform blind signal separation of the interfered mixed signal by means of BSS based on singular value and eigenvalue decomposition. Then, we image the different signals we have extracted. Finally, we extract the features of the image domain for the separated signals and set the information entropy threshold by the difference of information entropy to identify the jamming signal and the source signal and obtain the source signal. This method uses eigenvalue and singular value decomposition for BSS and extracts the image domain features of the signal after BSS by information entropy and identifies the source signal by information entropy thresholding. This method compensates for the uncertainty in the decomposition of the signal by means of BSS. The signal loss is minimal and the similarity of the separated signal and the original signal is very high. Simulated and measured data demonstrate the feasibility of this algorithm.

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 methods that can be done for the estimation of the number of source signals and separation of source signals using time‐frequency information are proposed as a method of blind source separation. In these methods, some independent conditions are assumed in a time‐frequency domain, and observed signals are expanded to time‐frequency domain using wavelet analysis. However, these methods are not considered phase differences (difference of distance) between source signals and observed signals. A new method is proposed. The method can be done not only for the source separation but also the specification of the locations of source signals considering phase differences. In this method, it is necessary to assume a rather stronger independent condition than former methods. But, on account of this assumption, a function that becomes a real value only when phase differences are coincidence in time‐frequency domain is determined. Using this function, first of all, the number of source signals is calculated, then the locations of source signals and source signals are calculated. The effectiveness of the method is shown using actual synthetic signals.

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 emerging field of fundamental research with a wide range of applications such as remote sensing, data communications, speech processing and medical diagnosis. It is motivated by practical scenarios that involve multi-sources and multi-sensors. The key objective of BSS is to retrieve the source signals without resorting to any a priori information about the source signals and the transmission channel. In this paper, a second order statistics based technique and the corresponding algorithm are presented to perform the blind separation of stationary or cyclostationary sources. Finally, a case study with real data having as subject dams displacements monitoring is presented.

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.

In order to overcome the problem of low accuracy and poor stability caused by the one-sided information blind separation analysis of the current communication channel interference suppression research methods, this paper proposes the optical communication network channel interference suppression method based on blind signal separation algorithm. The receiver unit, field programmable gate array (FPGA) unit, memory chip group and other modules are used to construct the channel signal acquisition system, and the collected signals are preprocessed by centralisation and whitening. Based on the signal preprocessing results, the blind separation of instantaneous linear mixed signals, blind separation of convolutional mixed signals and blind separation of sparse sources were comprehensively analysed to obtain the source signals and realise channel interference suppression of optical communication network. Experimental results show that this method has high interference precision, strong stability and good application prospect.