Blind source separation by weighted K-means clustering

Blind separation of sparse sources （BSSS） is discussed. The BSSS method based on the conventional K-means clustering is very fast and is also easy to implement. However, the accuracy of this method is generally not satisfactory. The contribution of the vector x（t） with different modules is theoretically proved to be unequal, and a weighted K-means clustering method is proposed on this grounds. The proposed algorithm is not only as fast as the conventional K-means clustering method, but can also achieve considerably accurate results, which is demonstrated by numerical experiments.

FREQUENCY OVERLAPPED SIGNAL IDENTIFICATION USING BLIND SOURCE SEPARATION

The concepts, principles and usages of principal component analysis （PCA） and independent component analysis （ICA） are interpreted. Then the algorithm and methodology of ICA-based blind source separation （BSS）, in which the pre-whitened based on PCA for observed signals is used, are researched. Aiming at the mixture signals, whose frequency components are overlapped by each other, a simulation of BSS to separate this type of mixture signals by using theory and approach of BSS has been done. The result shows that the BSS has some advantages what the traditional methodology of frequency analysis has not.

Neutron-gamma discrimination method based on blind source separation and machine learning

The discrimination of neutrons from gamma rays in a mixed radiation field is crucial in neutron detection tasks.Several approaches have been proposed to enhance the performance and accuracy of neutron-gamma discrimination.However,their performances are often associated with certain factors,such as experimental requirements and resulting mixed signals.The main purpose of this study is to achieve fast and accurate neutron-gamma discrimination without a priori information on the signal to be analyzed,as well as the experimental setup.Here,a novel method is proposed based on two concepts.The first method exploits the power of nonnegative tensor factorization(NTF)as a blind source separation method to extract the original components from the mixture signals recorded at the output of the stilbene scintillator detector.The second one is based on the principles of support vector machine(SVM)to identify and discriminate these components.In addition to these two main methods,we adopted the Mexican-hat function as a continuous wavelet transform to characterize the components extracted using the NTF model.The resulting scalograms are processed as colored images,which are segmented into two distinct classes using the Otsu thresholding method to extract the features of interest of the neutrons and gamma-ray components from the background noise.We subsequently used principal component analysis to select the most significant of these features wich are used in the training and testing datasets for SVM.Bias-variance analysis is used to optimize the SVM model by finding the optimal level of model complexity with the highest possible generalization performance.In this framework,the obtained results have verified a suitable bias–variance trade-off value.We achieved an operational SVM prediction model for neutron-gamma classification with a high true-positive rate.The accuracy and performance of the SVM based on the NTF was evaluated and validated by comparing it to the charge comparison method via figure of merit.The results indicate that the proposed approach has a superior discrimination quality(figure of merit of 2.20).

Blind source separation of ship-radiated noise based on generalized Gaussian model

When the distribution of the sources cannot be estimated accurately, the ICA algorithms failed to separate the mixtures blindly. The generalized Gaussian model （GGM） is presented in ICA algorithm since it can model non- Ganssian statistical structure of different source signals easily. By inferring only one parameter, a wide class of statistical distributions can be characterized. By using maximum likelihood （ML） approach and natural gradient descent, the learning rules of blind source separation （BSS） based on GGM are presented. The experiment of the ship-radiated noise demonstrates that the GGM can model the distributions of the ship-radiated noise and sea noise efficiently, and the learning rules based on GGM gives more successful separation results after comparing it with several conventional methods such as high order cumnlants and Gaussian mixture density function.

Online blind source separation based on joint diagonalization

A new algorithm is proposed for joint diagonalization. With a modified objective function, the new algorithm not only excludes trivial and unbalanced solutions successfully, but is also easily optimized. In addition, with the new objective function, the proposed algorithm can work well in online blind source separation （BSS） for the first time, although this family of algorithms is always thought to be valid only in batch-mode BSS by far. Simulations show that it is a very competitive joint diagonalization algorithm.

Blind source separation of multichannel electroencephalogram based on wavelet transform and ICA

Combination of the wavelet transform and independent component analysis （ICA） was employed for blind source separation （BSS） of multichannel electroencephalogram （EEG）. After denoising the original signals by discrete wavelet transform, high frequency components of some noises and artifacts were removed from the original signals. The denoised signals were reconstructed again for the purpose of ICA, such that the drawback that ICA cannot distinguish noises from source signals can be overcome effectively. The practical processing results showed that this method is an effective way to BSS of multichannel EEG. The method is actually a combination of wavelet transform with adaptive neural network, so it is also useful for BBS of other complex signals.

Algorithm for source recovery in underdetermined blind source separation based on plane pursuit

In order to achieve accurate recovery signals under the underdetermined circumstance in a comparatively short time,an algorithm based on plane pursuit(PP) is proposed. The proposed algorithm selects the atoms according to the correlation between received signals and hyper planes, which are composed by column vectors of the mixing matrix, and uses these atoms to recover source signals. Simulation results demonstrate that the PP algorithm has low complexity and higher accuracy as compared with basic pursuit(BP), orthogonal matching pursuit(OMP), and adaptive sparsity matching pursuit(ASMP) algorithms.

New Wavelet Threshold Denoising Method in Noisy Blind Source Separation

In general conditions, most blind source separation algorithms are established on noisy-free model and ignore the noise that affects the quality of separated sources. Firstly, this paper introduces an improved natural gradient algorithm based on bias removal technology to estimate the demixing matrix under noisy environment. Then the discrete wavelet transform technology is applied to the separated signals to further remove noise. In order to improve the separation effect, this paper analyzes the deficiency of hard threshold and soft threshold, and proposes a new wavelet threshold function based on the wavelet decomposition and reconfiguration. The simulations have verified that this method improves the signal noise ratio （SNR） of the separation results and the separation precision.

On-line blind source separation algorithm based on second order statistics

An on-line blind source separation （BSS） algorithm is presented in this paper under the assumption that sources are temporarily correlated signals. By using only some of the observed samples in a recursive calculation, the whitening matrix and the rotation matrix could be approximately obtained through the measurement of only one cost function. SimNations show goad performance of the algorithm.

The Research of Blind Source Separation (BSS) in Machinery Fault Diagnosis

Blind source separation (BSS) technology is very useful in many fields, such as communication, radar and so on. Because of the advantage of BSS that it can separate multi-sources even not knowing the mix-coefficient and the probability distribution, it can also be used in fault diagnosis. In this paper, we first use the BSS to deal with the sound from the machinery in fault diagnosis. We make a simulation of two sound sources and four sensors to test the result. Each source is a narrow-band source, which is composed of several sine waves. The result shows that the two sources can be well separated from the mixed signals. So we can draw a conclusion that BSS can improve the technology of sound fault diagnosis, especially in rotating machinery.

Under-determined blind source separation using complementary filter based sub-band division

This paper considers the blind source separation in under-determined case,when there are more sources than sensors.So many algorithms based on sparse in some signal representation domain,mostly in Time-Frequency(T-F) domain,are proposed in recent years.However,constrained by window effects and T-F resolution,these algorithms cannot have good performance in many cases.Considering most of signals in real world are band-limited signals,a new method based on sub-band division is proposed in this paper.Sensing signals are divided into different sub-bands by complementary filter firstly.Then,classical Independent Component Analysis(ICA) algorithms are applied in each sub-band.Next,based on each sub-band's estimation of mixing matrix,the mixing matrix is estimated with cluster analysis algorithms.After that,the sub-band signals are recovered using the estimation mixing matrix,and then,the resource signals are reconstructed by combining the related sub-band signals together.This method can recover the source signals if active sources at any sub-band do not exceed that of sensors.This is also a well mixing matrix estimating algorithm.Finally,computer simulation confirms the validity and good separation performance of this method.

For LEO Satellite Networks: Intelligent Interference Sensing and Signal Reconstruction Based on Blind Separation Technology

In LEO satellite communication networks,the number of satellites has increased sharply, the relative velocity of satellites is very fast, then electronic signal aliasing occurs from time to time. Those aliasing signals make the receiving ability of the signal receiver worse, the signal processing ability weaker,and the anti-interference ability of the communication system lower. Aiming at the above problems, to save communication resources and improve communication efficiency, and considering the irregularity of interference signals, the underdetermined blind separation technology can effectively deal with the problem of interference sensing and signal reconstruction in this scenario. In order to improve the stability of source signal separation and the security of information transmission, a greedy optimization algorithm can be executed. At the same time, to improve network information transmission efficiency and prevent algorithms from getting trapped in local optima, delete low-energy points during each iteration process. Ultimately, simulation experiments validate that the algorithm presented in this paper enhances both the transmission efficiency of the network transmission system and the security of the communication system, achieving the process of interference sensing and signal reconstruction in the LEO satellite communication system.

Sparse representation and blind source separation of ill-posed mixtures

Bofill et al. discussed blind source separation （BSS） of sparse signals in the case of two sensors. However, as Bofill et al. pointed out, this method has some limitation. The potential function they introduced is lack of theoretical basis. Also the method could not be extended to solve the problem in the case of more than three sensors. In this paper, instead of the potential function method, a K-PCA method （combining K-clustering with PCA） is proposed. The new method is easy to be used in the case of more than three sensors. It is easy to be implemented and can provide accurate estimation of mixing matrix. Some criterion is given to check the effect of the mixing matrix A. Some simulations illustrate the availability and accuracy of the method we proposed.

Grading learning for blind source separation

By generalizing the learning rate parameter to a learning rate matrix, this paper proposes a grading learning algorithm for blind source separation. The whole learning process is divided into three stages: initial stage, capturing stage and tracking stage. In different stages, different learning rates are used for each output component, which is determined by its dependency on other output components. It is shown that the grading learning algorithm is equivariant and can keep the separating matrix from becoming singular. Simulations show that the proposed algorithm can achieve faster convergence, better steady-state performance and higher numerical robustness, as compared with the existing algorithms using fixed, time-descending and adaptive learning rates.

Underdetermined DOA estimation and blind separation of non-disjoint sources in time-frequency domain based on sparse representation method

This paper deals with the blind separation of nonstation-ary sources and direction-of-arrival （DOA） estimation in the under-determined case, when there are more sources than sensors. We assume the sources to be time-frequency （TF） disjoint to a certain extent. In particular, the number of sources presented at any TF neighborhood is strictly less than that of sensors. We can identify the real number of active sources and achieve separation in any TF neighborhood by the sparse representation method. Compared with the subspace-based algorithm under the same sparseness assumption, which suffers from the extra noise effect since it can-not estimate the true number of active sources, the proposed algorithm can estimate the number of active sources and their cor-responding TF values in any TF neighborhood simultaneously. An-other contribution of this paper is a new estimation procedure for the DOA of sources in the underdetermined case, which combines the TF sparseness of sources and the clustering technique. Sim-ulation results demonstrate the validity and high performance of the proposed algorithm in both blind source separation （BSS） and DOA estimation.

Natural gradient-based recursive least-squares algorithm for adaptive blind source separation

This paper focuses on the problem of adaptive blind source separation (BSS). First, a recursive least-squares (RLS) whitening algorithm is proposed. By combining it with a natural gradient-based RLS algorithm for nonlinear principle component analysis (PCA), and using reasonable approximations, a novel RLS algorithm which can achieve BSS without additional pre-whitening of the observed mixtures is obtained. Analyses of the equilibrium points show that both of the RLS whitening algorithm and the natural gradient-based RLS algorithm for BSS have the desired convergence properties. It is also proved that the combined new RLS algorithm for BSS is equivariant and has the property of keeping the separating matrix from becoming singular. Finally, the effectiveness of the proposed algorithm is verified by extensive simulation results.

Blind source separation with unknown and dynamically changing number of source signals

The contrast function remains to be an open problem in blind source separation （BSS） when the number of source signals is unknown and/or dynamically changed. The paper studies this problem and proves that the mutual information is still the contrast function for BSS if the mixing matrix is of full column rank. The mutual information reaches its minimum at the separation points, where the random outputs of the BSS system are the scaled and permuted source signals, while the others are zero outputs. Using the property that the transpose of the mixing matrix and a matrix composed by m observed signals have the indentical null space with probability one, a practical method, which can detect the unknown number of source signals n, ulteriorly traces the dynamical change of the sources number with a few of data, is proposed. The effectiveness of the proposed theorey and the developed novel algorithm is verified by adaptive BSS simulations with unknown and dynamically changing number of source signals.

TBSSvis:Visual analytics for Temporal Blind Source Separation

Temporal Blind Source Separation(TBSS)is used to obtain the true underlying processes from noisy temporal multivariate data,such as electrocardiograms.TBSS has similarities to Principal Component Analysis(PCA)as it separates the input data into univariate components and is applicable to suitable datasets from various domains,such as medicine,finance,or civil engineering.Despite TBSS’s broad applicability,the involved tasks are not well supported in current tools,which offer only text-based interactions and single static images.Analysts are limited in analyzing and comparing obtained results,which consist of diverse data such as matrices and sets of time series.Additionally,parameter settings have a big impact on separation performance,but as a consequence of improper tooling,analysts currently do not consider the whole parameter space.We propose to solve these problems by applying visual analytics(VA)principles.Our primary contribution is a design study for TBSS,which so far has not been explored by the visualization community.We developed a task abstraction and visualization design in a user-centered design process.Task-specific assembling of well-established visualization techniques and algorithms to gain insights in the TBSS processes is our secondary contribution.We present TBSSvis,an interactive web-based VA prototype,which we evaluated extensively in two interviews with five TBSS experts.Feedback and observations from these interviews show that TBSSvis supports the actual workflow and combination of interactive visualizations that facilitate the tasks involved in analyzing TBSS results.

Study and simulation of video communications under wireless environment based on blind source separation

A new scheme is proposed to separate several compressed video signals transferred in multiple wireless channels using the blind source separation method.The scheme selects IEEE 802.11b and XVID compression as the wireless communications channel and MPEG-4 video compression,respectively.A simulation model is then made for the video communications under a wireless environment.The model can separate several video sig-nals using blind source separation.Simulations show that the normalized whiten plus cyclic whiten based on cyclo-stationary(NWCW-CS)algorithm based upon the cyclo-stationary characteristics of signals has the best separation performance and fast convergence.Besides,the algorithm can solve the mixing of video signals.The image of the transferred video signals decompressed by XVID is nearly consistent with the source ones.The new method meets the requirement of real-time video communications.

Blind source separation algorithm for communication complex signals in communication reconnaissance

Most blind source separation algorithms are only applicable to real signals,while in communication reconnaissance processed signals are complex.To solve this problem,a blind source separation algorithm for communication complex signals is deduced,which is obtained by adopting the Kullback-Leibler divergence to measure the signals’independence.On the other hand,the performance of natural gradient is better than that of stochastic gradient,thus the natural gradient of the cost function is used to optimize the algorithm.According to the conclusion that the signal’s mixing matrix after whitening is orthogonal,we deduce the iterative algorithm by constraining the separating matrix to an orthogonal matrix.Simulation results show that this algorithm can efficiently separate the source signals even in noise circumstances.