A Beamformer-Particle Filter Framework for Localization of Correlated EEG Sources

A new data covariance matrix estimation for improving minimum variance brain source localization

Data with finite samples results in accuracy and robustness reduction of data covariance matrix estimation, which in turn results in performance reduction of minimum variance beamformer (MVB) for brain source localization (BSL). General linear combination (GLC) and convex combination (CC) are methods of interest for data covariance matrix estimation and increasing its accuracy and robustness because their scalar coefficients are obtained automatically and adaptively. However, based on our best knowledge, the applicability of GLC and CC algorithms has not been investigated for BSL to inform us about their performance. In this paper, we have two goals: 1) Investigation of GLC and CC covariance matrices applications for BSL is carried out using various simulated MEG scenarios and real MEG and clinical epilepsy data; 2) Modified GLC and CC are developed for more accurate and robust estimation of data covariance matrix when data with finite samples is available. In the modified versions, the scalar coefficients are replaced by diagonal matrix form coefficients. These matrix form coefficients are computed using the Hadamard product and mean square error concept. The evaluations show that the CC and modified CC based MVBs are not robust for BSL due to very small values of coefficients. Based on the simulated, real, and clinical data results, it can be stated that the modified GLC is significantly superior to conventional GLC in terms of localization error, spatial resolution (all z < -2; all p-values < 0.001), and offering reliable results. Also, the proposed GLC offers fewer missed sources and less sensitivity to the depth biasing problem, particularly in a high signal-to-noise ratio. In conclusion, it can be said that the covariance matrix of modified GLC which is user-free and robust against the finite data samples can improve the MVB performance for BSL in terms of localization error and spatial resolution.

Developing a Multi-channel Beamformer by Enhancing Spatially Constrained ICA for Recovery of Correlated EEG Sources

Background:

Brain source imaging based on electroencephalogram (EEG) data aims to recover the neuron populations’ activity producing the scalp potentials. This procedure is known as the EEG inverse problem. Recently, beamformers have gained a lot of consideration in the EEG inverse problem.

Objective:

Beamformers lack acceptable performance in the case of correlated brain sources. These sources happen when some regions of the brain have simultaneous or correlated activities such as auditory stimulation or moving left and right extremities of the body at the same time. In this paper, we have developed a multichannel beamformer robust to correlated sources.

Material and Methods:

In this simulation study, we have looked at the problem of brain source imaging and beamforming from a blind source separation point of view. We focused on the spatially constraint independent component analysis (scICA) algorithm, which generally benefits from the pre-known partial information of mixing matrix, and modified the steps of the algorithm in a way that makes it more robust to correlated sources. We called the modified scICA algorithm Multichannel ICA based EEG Beamformer (MIEB).

Results:

We evaluated the proposed algorithm on simulated EEG data and compared its performance quantitatively with three algorithms scICA, linearly-constrained minimum-variance (LCMV) and Dual-Core beamformers; it is considered that the latter is specially designed to reconstruct correlated sources.

Conclusion:

The MIEB algorithm has much better performance in terms of normalized mean squared error in recovering the correlated/uncorrelated sources both in noise free and noisy synthetic EEG signals. Therefore, it could be used as a robust beamformer in recovering correlated brain sources.

Multiple dipole source localization of EEG measurements using particle filter with partial stratified resampling

Tracking and detection of neural activity has numerous applications in the medical research field. By considering neural sources, it can be monitored by electroencephalography (EEG). In this paper, we focus primarily on developing advanced signal processing methods for locating neural sources. Due to its high performance in state estimation and tracking, particle filter was used to locate neural sources. However, particle degeneracy limits the performance of particle filters in the most utmost situations. A few resampling methods were subsequently proposed to ease this issue. These resampling methods, however, take on heavy computational costs. In this article, we aim to investigate the Partial Stratified Resampling algorithm which is time-efficient that can be used to locate neural sources and compare them to conventional resampling algorithms. This work is aimed at reflecting on the capabilities of various resampling algorithms and estimating the performance of locating neural sources. Simulated data and real EEG data are used to conduct evaluation and comparison experiments.

EEG dipole source localization with information criteria for multiple particle filters

Electroencephalography (EEG) is a non-invasive brain imaging technique that describes neural electrical activation with good temporal resolution. Source localization is required for clinical and functional interpretations of EEG signals, and most commonly is achieved via the dipole model; however, the number of dipoles in the brain should be determined for a reasonably accurate interpretation. In this paper, we propose a dipole source localization (DSL) method that adaptively estimates the dipole number by using a novel information criterion. Since the particle filtering process is nonparametric, it is not clear whether conventional information criteria such as Akaike's information criterion (AIC) and Bayesian information criterion (BIC) can be applied. In the proposed method, multiple particle filters run in parallel, each of which respectively estimates the dipole locations and moments, with the assumption that the dipole number is known and fixed; at every time step, the most predictive particle filter is selected by using an information criterion tailored for particle filters. We tested the proposed information criterion first through experiments on artificial datasets; these experiments supported the hypothesis that the proposed information criterion would outperform both AIC and BIC. We then analyzed real human EEG datasets collected during an auditory short-term memory task using the proposed method. We found that the alpha-band dipoles were localized to the right and left auditory areas during the auditory short-term memory task, which is consistent with previous physiological findings. These analyses suggest the proposed information criterion can work well in both model and real-world situations.

Reducing the Computational Complexity of EEG Source Localization With Cortical Patch Decomposition and Optimal Electrode Selection

OBJECTIVE

Real-time implementation of EEG source localization can be employed in a broad area of applications such as clinical diagnosis of neurologic diseases and brain-computer interface. However, a power-efficient, low-complexity, and real-time implementation of EEG source localization is still challenging due to extensive iterations in the solutions. In this study, two techniques are introduced to reduce the computational burden of the subspace-based MUltiple SIgnal Classification (MUSIC) algorithm.

METHODS

To shrink the exhaustive search inherent in MUSIC, the cortex is parsed into cortical regions. A novel nomination procedure involving a dictionary learning step will pick a number of regions to be searched for the active sources. In addition, a new electrode selection algorithm based on the Cramer-Rao bound of the errors is introduced to pick the best set of an arbitrary number of electrodes out of the total.

RESULTS

The performance of the proposed techniques were evaluated using simulated EEG signal under variation of different parameters such as the number of nominated regions, the signal to noise ratio, and the number of electrodes. The proposed techniques can reduce the computational complexity by up to $90\%$. Furthermore, the proposed techniques were tested on EEG data from an auditory oddball experiment.

CONCLUSION

A good concordance was observed in the comparison of the topographies and the localization errors derived from the proposed technique and regular MUSIC.

SIGNIFICANCE

Such reduction can be exploited in the real-time, long-run, and mobile monitoring of cortical activity for clinical diagnosis and research purposes.