Fixed-point Independent Component Analysis Algorithm Research Articles

Performance analysis for complex-valued FastICA and its improvement based on the Tukey M-estimator

Independent component analysis (ICA) is increasingly utilized to modern digital signal processing. Complex-valued FastICA, a fast fixed-point algorithm for ICA, is one of the most non-trivial algorithms for solving the ICA problems in the complex domain. Hitherto, there have been several attempts to give performance analysis for complex-valued FastICA. Rigorous theoretical analysis, however, still has room for improvement further. Consequently, the purposes of this paper are threefold: Firstly, the uniformity of the complex-valued FastICA estimator is constructed for the first time. Secondly, the stability of the complex-valued ICA algorithm is rigorously deduced based on the augmented generating matrix. Meanwhile, the local convergence of complex-valued FastICA algorithm is derived based on circular source signals. Finally, for improving the performance of separation, we select a novel alternative for nonlinearity based on the Tukey M-estimator in the complex-valued FastICA algorithm. Further, we prove the existence of local optimal solution and stability of the complex ICA problem based on the Tukey M-estimator. Simulations are presented to demonstrate the accuracy of our analysis. Additionally, the experimental results with synthetic data and complex-valued wind signal show the superiorities of the improved method.

A Comparative Study of Blind Source Separation for Bioacoustics Sounds based on FastICA, PCA and NMF

Blind Source Separation (BSS) is a task of separating a set of source signals from mixed signal without (or very little information) of both the sources and the mixing process. This paper addresses the problem of BSS in bio-acoustic mixed signals. In a noisy acoustic environment, animal species recognition based on vocalization remains a challenging task. In order to robustly recognize the specific species, the source signals of interest need to be separated from the mixed signals. This separation process is a significant pre-processing step before the recognition process takes place. In this paper, three different source separation methods namely Fast Fixed-Point Independent Component Analysis algorithms (FastICA), Principal Component Analysis (PCA) and Non-Negative Matrix Factorization (NMF) are implemented. In this experiment, the mixtures of frog sound signals are used as input. The quality of separated source signals using FastICA, PCA and NMF algorithms are compared and evaluated according to BSS_EVAL toolbox metrics. These metrics consist of signal to distortion ratio (SDR), signal to interference ratio (SIR) and signal to artifacts ratio (SAR). The results show that FastICA with negentropy technique for finding a maximum non-gaussianity has the best performances in separating mixed signals.

CHANGE DETECTION OF MULTI‐TEMPORAL REMOTE SENSING IMAGES BASED ON CONTOURLET TRANSFORM AND ICA

AbstractIn order to improve the accuracy and computational efficiency of change detection of multi‐temporal remote sensing images, a change detection algorithm based on contourlet transform and independent component analysis (ICA) is proposed. Firstly, multi‐scale decomposition of image data is performed by using contourlet transform with multi‐scale, directionality and anisotropy. Then independent component analysis is carried out for the decomposed data. And the independent data components are separated by the improved fixed point ICA algorithm based on Newton iteration. Next the separated data components are transformed into image components. Finally, change detection is achieved by threshold segmentation and filtering for change image components. The experimental results show that, compared with the existing three change detection algorithms such as the algorithm based on PCA, the algorithm based on ICA and the algorithm based on wavelet transform and ICA, the proposed algorithm in this paper more effectively separates change information and reduces computational complexity. The obtained change image has higher accuracy and strong robustness with respect to the background.

Fixed-point ICA algorithm for blind separation of complex mixtures containing both circular and noncircular sources

Fixed-point algorithms are widely used for independent component analysis (ICA) owing to its good convergence. However, most existing complex fixed-point ICA algorithms are limited to the case of circular sources and result in phase ambiguity, that restrict the practical applications of ICA. To solve these problems, this paper proposes a two-stage fixed-point ICA (TS-FPICA) algorithm which considers complex signal model. In this algorithm, the complex signal model is converted into a new real signal model by utilizing the circular coefficients contained in the pseudo-covariance matrix. The algorithm is thus valid to noncircular sources. Moreover, the ICA problem under the new model is formulated as a constrained optimization problem, and the real fixed-point iteration is employed to solve it. In this way, the phase ambiguity resulted by the complex ICA is avoided. The computational complexity and convergence property of TS-FPICA are both analyzed theoretically. Simulation results show that the proposed algorithm has better separation performance and without phase ambiguity in separated signals compared with other algorithms. TS-FPICA convergences nearly fast as the other fixed-point algorithms, but far faster than the joint diagonalization method, e.g. joint approximate diagonalization of eigenmatrices (JADE).

Trajectory optimisation method by using independent component analysis for MIMO‐OTHR target tracking

Traditional sky-wave over-the-horizon radar (OTHR) target tracking algorithms, such as multipath probabilistic data association, can achieve good performance if the multipath environment clutter is not strong enough. The computation complexity and tracking performance of these algorithms can be further improved by multiple-input multiple-output (MIMO) radar technology owing to its capability to utilise transmitting and receiving diversities. However, multipath propagation is still considered to degrade the performance because of the strong ionosphere and sea clutter. To deal with the interference of strong clutter in a multipath environment, a tracking trajectory optimisation method is proposed by applying the fast and robust fixed-point independent component analysis algorithm which uses the projection pursuit approach to separate clutter and a true target moving trajectory from the received signals. Numerical simulations demonstrate the feasibility of the method, and it also shows that the multipath measurements can be utilised for MIMO-OTHR target tracking.

Application of neural networks with novel independent component analysis methodologies to a Prussian blue modified glassy carbon electrode array

Sodium potassium absorption ratio (SPAR) is an important measure of agricultural water quality, wherein four exchangeable cations (K+, Na+, Ca2+ and Mg2+) should be simultaneously determined. An ISE-array is suitable for this application because its simplicity, rapid response characteristics and lower cost. However, cross-interferences caused by the poor selectivity of ISEs need to be overcome using multivariate chemometric methods. In this paper, a solid contact ISE array, based on a Prussian blue modified glassy carbon electrode (PB-GCE), was applied with a novel chemometric strategy. One of the most popular independent component analysis (ICA) methods, the fast fixed-point algorithm for ICA (fastICA), was implemented by the genetic algorithm (geneticICA) to avoid the local maxima problem commonly observed with fastICA. This geneticICA can be implemented as a data preprocessing method to improve the prediction accuracy of the Back-propagation neural network (BPNN). The ISE array system was validated using 20 real irrigation water samples from South Australia, and acceptable prediction accuracies were obtained.

On the convergence of ICA algorithms with weighted orthogonal constraint

A kind of weighted orthogonal constrained independent component analysis (ICA) algorithms with weighted orthogonalization for achieving this constraint is proposed recently. It has been proved in the literature that weighted orthogonal constrained ICA algorithms keep the equivariance property and have much better convergence speed, separation ability and steady state misadjustment, but the convergence is not yet analyzed in the published literature. The goal of this paper is to fill this gap. Firstly, a characterization of the stationary points corresponding to these algorithms using symmetric Minimum Distance Weighted Unitary Mapping (MDWUM) for achieving the weighted orthogonalization is obtained. Secondly, the monotonic convergence of the weighted orthogonal constrained fixed point ICA algorithms using symmetric MDWUM for convex contrast function is proved, which is further extended to nonconvex contrast functions case by adding a weighted orthogonal constraint term onto the contrast function. Together with the boundedness of contrast function, the convergence of fixed point ICA algorithms with weighted orthogonal constraint using symmetric MDWUM is implied. Simulation experiments results show that the adaptive ICA algorithms using symmetric MDWUM are better in terms of accuracy than the ones with pre-whitening, and the fixed-point ICA algorithms using symmetric MDWUM converge monotonically.

A Novel Floating Point Fast Confluence Adaptive Independent Component Analysis for Signal Processing Applications

Independent component analysis (ICA) is a technique that separates the independent source signals from their mixtures by minimizing the statistical dependence between components. This paper presents a floating point implementation of a novel fast confluence adaptive independent component analysis (FCAICA) technique with reduced number of iterations that provides the high convergence speed. Fixed point ICA algorithms cover only smaller range of numbers. To handle large as well as tiny numbers and hence to improve the dynamic range of the signal values, floating point operations are performed in ICA. The high convergence speed is achieved by a novel optimization scheme that adaptively changes the weight vector based on the kurtosis value. To validate the performance of the proposed FCAICA, simulation and synthesis are performed with super-gaussian mixtures and sub Gaussian mixtures and experimental results provided. The proposed FCAICA processor separates the super-Gaussian signals with a maximum operating frequency of 2.91MHz with improved convergence speed.

Artifact Removal from Biosignal using Fixed Point ICA Algorithm for Pre-processing in Biometric Recognition

In the modern world of automation, biological signals, especially Electroencephalogram (EEG) and Electrocardiogram (ECG), are gaining wide attention as a source of biometric information. Earlier studies have shown that EEG and ECG show versatility with individuals and every individual has distinct EEG and ECG spectrum. EEG (which can be recorded from the scalp due to the effect of millions of neurons) may contain noise signals such as eye blink, eye movement, muscular movement, line noise, etc. Similarly, ECG may contain artifact like line noise, tremor artifacts, baseline wandering, etc. These noise signals are required to be separated from the EEG and ECG signals to obtain the accurate results. This paper proposes a technique for the removal of eye blink artifact from EEG and ECG signal using fixed point or FastICA algorithm of Independent Component Analysis (ICA). For validation, FastICA algorithm has been applied to synthetic signal prepared by adding random noise to the Electrocardiogram (ECG) signal. FastICA algorithm separates the signal into two independent components, i.e. ECG pure and artifact signal. Similarly, the same algorithm has been applied to remove the artifacts (Electrooculogram or eye blink) from the EEG signal.

A comparative study of complex gradient and fixed-point ICA algorithms for interference suppression in static and dynamic channels

Separation of complex signals using independent component analysis (ICA) is an area of extensive research. Several gradient and fixed-point complex ICA algorithms have been proposed in this regard. In this contribution, the performance of the recently developed complex ICA with individual adaptation (C-IA-ICA) is compared to the most recent gradient optimization KM algorithm (KM-G) and fixed-point complex fast-ICA (CF-ICA) algorithm. The algorithms are tested in interference suppression for QPSK based receivers, in both static and dynamic channel conditions. In addition, two simulation scenarios are presented. In the first case, the interferer is another QPSK signal, while in the second the interferer is a 16-QAM signal. In static conditions, the CF-ICA has the fastest convergence with high interference suppression. However, in dynamic scenarios frequently encountered in practice, its convergence speed is greatly affected. The complex IA-ICA achieves good interference suppression in both static and dynamic channels without a significant effect on its convergence speed. The KM-G, while not diverging, in both static and dynamic channel situations, is less effective in interference suppression, in contrast to the CF-ICA and C-IA-ICA which achieve acceptable interference suppression in both cases.

Effect of Central Limit Theorem non-compliance on blind separation of speech by negentropy maximization

In this paper the blind separation of speech signals from their convoluted mixtures using frequency domain fixed-point independent component analysis algorithm, based on negentropy maximization, is presented. We also discuss fundamental problems of fixed-point ICA by negentropy maximization arising in the separation of the speech signal due to disobedience of the Central Limit Theorem (CLT) by the mixed speech data in the frequency domain. The experimental evidences show that CLT failure is happening due to the spectral sparseness of sources. We also present a blind method to mitigate the negative effects of this by combining null beamforming with the ICA. This combination gives a good result under the low reverberation conditions.