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

Area of Science:

• Neuroscience
• Biomedical Engineering
• Signal Processing

Background:

• The electroencephalographic (EEG) inverse problem is inherently ill-posed due to the Helmholtz theorem and limited observational data.
• EEG recordings are often contaminated by significant outliers from head or eye movements, in addition to background neural activity.

Purpose of the Study:

• To develop a robust EEG source imaging algorithm capable of handling noise and outliers for accurate brain neural generator localization.
• To address the challenges posed by sparse activations during high cognitive processing.

Main Methods:

• Proposed a novel algorithm, LAPPS (Least Absolute -P Penalized Solution), utilizing an -loss for residual errors to mitigate outlier effects.
• Employed a 0.5-penalty norm to achieve sparse source recovery and suppress Gaussian noise.
• Solved the optimization problem using a modified Alternating Direction Method of Multipliers (ADMM) algorithm.

Main Results:

• Simulation studies demonstrated LAPPS outperformed existing methods (WMNE, -norm, sLORETA, FOCUSS) in recovering sparse signals across various configurations and SNRs.
• LAPPS accurately localized brain neural generators in a real visual oddball experiment, showing sparse activations consistent with prior EEG and fMRI findings.

Conclusions:

• LAPPS presents a robust and effective sparse method for EEG source imaging, providing a valuable tool for investigating brain neural generators.
• The algorithm efficiently alleviates noise, recovers sparse sources, and maintains low computational complexity.