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

Objective: The electroencephalographic (EEG) inverse problem is ill-posed owing to the electromagnetism Helmholtz theorem and since there are fewer observations than the unknown variables. Apart from the strong background activities (ongoing EEG), evoked EEG is also inevitably contaminated by strong outliers caused by head movements or ocular movements during recordings. Methods: Considering the sparse activations during high cognitive processing, we propose a novel robust EEG source imaging algorithm, least absolute $l$ -P (0<p<1) penalized solution (LAPPS), which employs the ${l_1}$ -loss for the residual error to alleviate the effect of outliers and another ${l_p}$ -penalty norm (p = 0.5) to obtain sparse sources while suppressing Gaussian noise in EEG recordings. The resulting optimization problem is solved using a modified alternating direction method of multipliers algorithm. Results: Simulation study was performed to recover sparse signals of randomly selected sources using LAPPS and various methods commonly used for EEG source imaging including weighted minimum norm estimate, ${l_1}$ -norm, standardized low resolution electromagnetic tomography and focal underdetermined system solver solution. The simulation comparison quantitatively demonstrates that LAPPS obtained the best performances in all the conducted simulations for various dipoles configurations under various signal-to-noise ratio on a realistic head model. Moreover, in the localization of brain neural generators in a real visual oddball experiment, LAPPS obtained sparse activations consistent with previous findings revealed by EEG and functional magnetic resonance imaging. Conclusion: This study demonstrates a potentially useful sparse method for EEG source imaging, creating a platform for investigating the brain neural generators. Significance: This method alleviates the effect of noise and recovers sparse sources while maintaining a low computational complexity due to the cheap matrix-vector multiplication. [ABSTRACT FROM AUTHOR]