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Sparse EEG Source Localization Using LAPPS: Least Absolute l -P (0 < p < 1) Penalized Solution

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Sparse EEG Source Localization Using LAPPS: Least Absolute <em>l</em> -P (0<p<1) Penalized Solution

The ill-posed nature of electroencephalogram-EEG (or related magnetoencephalogram-MEG) poses a great challenge in neuroimaging. Considering that EEG electrode sensors measure the scalp potentials rather than directly measuring neural activities inside the head, a lot of research in recent years has focused on EEG source imaging algorithms in a bid to infer the activated brain regions due to its importance in neuroscience research and clinical application.

However, EEG is usually inevitably contaminated by outliers due to the eye blinks or head movements during EEG recordings. A vast majority of EEG source localization approaches utilize the popular L2-norm loss function yet it has a tendency of exaggerating the outlier effect owing to the square property of the L2 norm. Recently, the L1-loss function has been proven to be less sensitive to outliers as compared to the quadratic function. Consequently, in this work, we propose a novel robust and sparse approach for EEG source imaging known as the Least Absolute l-P (0<p<1) Penalized Solution (LAPPS) which simultaneously adopts an l 1-loss function to measure the residual error and an Lp-penalty term (p=0.5) to constrain the EEG sources. This method utilizes the alternating direction method of multipliers (ADMM) approach to efficiently solve the optimization problem.

The simulation results in various dipoles configurations under various SNRs on a realistic head model prove the superiority of LAPPS over other EEG source imaging methods including the l1 -norm, sLORETA, WMNE and FOCUSS. Moreover, in the localization of brain neural generators in a real visual oddball experiment, LAPPS also obtained sparse activations consistent with previous findings revealed by EEG and fMRI. This work demonstrates a potentially useful sparse method for EEG source imaging, creating a platform for investigating the brain neural generators which will facilitate practical clinical applications and neuroscience research.

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