EEG source distribution localization using minimum-product and CRESO criteria for Tikhonov regularization.

Area of Science:

• Neuroscience
• Biomedical Engineering
• Computational Science

Background:

• Electroencephalographic (EEG) inverse problems are inherently ill-posed.
• High condition numbers in transfer matrices complicate accurate source localization.
• Noise in voltage measurements significantly impacts the reliability of EEG data.

Purpose of the Study:

• To reconstruct simulated cortical source distributions using a novel formulation.
• To evaluate the performance of Tikhonov regularization technique (TRT) in solving discrete EEG inverse problems.
• To compare the efficacy of the CRESO and MP criteria for determining optimal regularization parameters.

Main Methods:

• Simulated cortical source distributions were reconstructed.
• The Tikhonov regularization technique (TRT) was applied to address ill-posed inverse problems.
• The composite residual and smoothing operator (CRESO) and minimum-product (MP) criteria were used to approximate optimal regularization parameters.

Main Results:

• The TRT successfully reconstructed extended intracranial source distributions with separate source and sink positions.
• The CRESO criterion demonstrated significantly better performance than the MP criterion when Gaussian measurement noise exceeded 10%.
• Extending both criteria to include boundary regularization parameter values improved their approximation accuracy.

Conclusions:

• The Tikhonov regularization technique provides a robust method for solving EEG inverse problems.
• The CRESO criterion is a more reliable method for selecting regularization parameters in noisy EEG data compared to the MP criterion.
• Accurate reconstruction of cortical sources is achievable even with substantial levels of measurement noise.