BMICA-independent component analysis based on B-spline mutual information estimator

The information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. Its estimation however using B-Spline has not been used before in creating an approach for Independent Component Analysis. In this paper we present a B-Spline estimator for mutual information to find the independent components in mixed signals. Tested using electroencephalography (EEG) signals the resulting BMICA (B-Spline Mutual Information Independent Component Analysis) exhibits better performance than the standard Independent Component Analysis algorithms of FastICA, JADE, SOBI and EFICA in similar simulations. BMICA was found to be also more reliable than the 'renown' FastICA

Orthogonal Extended Infomax Algorithm

The extended infomax algorithm for independent component analysis (ICA) can separate sub- and super-Gaussian signals but converges slowly as it uses stochastic gradient optimization. In this paper, an improved extended infomax algorithm is presented that converges much faster. Accelerated convergence is achieved by replacing the natural gradient learning rule of extended infomax by a fully-multiplicative orthogonal-group based update scheme of the unmixing matrix leading to an orthogonal extended infomax algorithm (OgExtInf). Computational performance of OgExtInf is compared with two fast ICA algorithms: the popular FastICA and Picard, a L-BFGS algorithm belonging to the family of quasi-Newton methods. Our results demonstrate superior performance of the proposed method on small-size EEG data sets as used for example in online EEG processing systems, such as brain-computer interfaces or clinical systems for spike and seizure detection.Comment: 17 pages, 6 figure

Optimization of a hardware/software coprocessing platform for EEG eyeblink detection and removal

The feasibility of implementing a real-time system for removing eyeblink artifacts from electroencephalogram (EEG) recordings utilizing a hardware/software coprocessing platform was investigated. A software based wavelet and independent component analysis (ICA) eyeblink detection and removal process was extended to enable variation in its processing parameters. Exploiting the efficiency of hardware and the reconfigurability of software, it was ported to a field programmable gate array (FPGA) development platform which was found to be capable of implementing the revised algorithm, although not in real-time. The implemented hardware and software solution was applied to a collection of both simulated and clinically acquired EEG data with known artifact and waveform characteristics to assess its speed and accuracy. Configured for optimal accuracy in terms of minimal false positives and negatives as well as maintaining the integrity of the underlying EEG, especially when encountering EEG waveform patterns with an appearance similar to eyeblink artifacts, the system was capable of processing a 10 second EEG epoch in an average of 123 seconds. Configured for efficiency, but with diminished accuracy, the system required an average of 34 seconds. Varying the ICA contrast function showed that the gaussian nonlinearity provided the best combination of reliability and accuracy, albeit with a long execution time. The cubic nonlinearity was fast, but unreliable, while the hyperbolic tangent contrast function frequently diverged. It is believed that the utilization of programmable logic with increased logic capacity and processing speed may enable this approach to achieve the objective of real-time operation

Detection and removal of eyeblink artifacts from EEG using wavelet analysis and independent component analysis

Electrical signals generated by brain activity that are measured by the electroencephalogram can be distorted by electrical activity originating from eyeblinks and eye movements. This thesis proposes a new technique to identify and remove eyeblink artifacts from EEG data. An algorithm using a combination of wavelet analysis and independent component analysis (ICA) is implemented to detect the temporal location of the eyeblink artifact and eliminate it without compromising the integrity of the primary EEG data. The discrete wavelet transform is performed on 10 second epochs of data to detect the occurrence of ocular artifact. ICA is used to separate out the independent components within the data and the temporal locations of the eyeblink are used to remove the artifact and reconstruct the EEG data without that source of distortion. The results obtained indicate that the technique implemented may be robust enough to effectively process EEG data and is capable of removing eyeblink artifacts successfully when they are prominent and the data does not contain a great deal of movement artifact. The results show an 88.68% detection rate, a false positive rate of 4.03%, and an 87.23% removal rate for all eyeblinks that were accurately detected. The statistics obtained compared favorably with work done by others in this field of investigation

Adaptive signal processing algorithms for noncircular complex data

The complex domain provides a natural processing framework for a large class of signals encountered in communications, radar, biomedical engineering and renewable energy. Statistical signal processing in C has traditionally been viewed as a straightforward extension of the corresponding algorithms in the real domain R, however, recent developments in augmented complex statistics show that, in general, this leads to under-modelling. This direct treatment of complex-valued signals has led to advances in so called widely linear modelling and the introduction of a generalised framework for the differentiability of both analytic and non-analytic complex and quaternion functions. In this thesis, supervised and blind complex adaptive algorithms capable of processing the generality of complex and quaternion signals (both circular and noncircular) in both noise-free and noisy environments are developed; their usefulness in real-world applications is demonstrated through case studies. The focus of this thesis is on the use of augmented statistics and widely linear modelling. The standard complex least mean square (CLMS) algorithm is extended to perform optimally for the generality of complex-valued signals, and is shown to outperform the CLMS algorithm. Next, extraction of latent complex-valued signals from large mixtures is addressed. This is achieved by developing several classes of complex blind source extraction algorithms based on fundamental signal properties such as smoothness, predictability and degree of Gaussianity, with the analysis of the existence and uniqueness of the solutions also provided. These algorithms are shown to facilitate real-time applications, such as those in brain computer interfacing (BCI). Due to their modified cost functions and the widely linear mixing model, this class of algorithms perform well in both noise-free and noisy environments. Next, based on a widely linear quaternion model, the FastICA algorithm is extended to the quaternion domain to provide separation of the generality of quaternion signals. The enhanced performances of the widely linear algorithms are illustrated in renewable energy and biomedical applications, in particular, for the prediction of wind profiles and extraction of artifacts from EEG recordings

Nonparametric Independent Component Analysis for the Sources with Mixed Spectra

Independent component analysis (ICA) is a blind source separation method to recover source signals of interest from their mixtures. Most existing ICA procedures assume independent sampling. Second-order-statistics-based source separation methods have been developed based on parametric time series models for the mixtures from the autocorrelated sources. However, the second-order-statistics-based methods cannot separate the sources accurately when the sources have temporal autocorrelations with mixed spectra. To address this issue, we propose a new ICA method by estimating spectral density functions and line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated by maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through simulation experiments and an EEG data application. The numerical results indicate that our approach outperforms existing ICA methods, including SOBI algorithms. In addition, we investigate the asymptotic behavior of the proposed method.Comment: 27 pages, 10 figure