# FEM-based Scalp-to-Cortex data mapping via the solution of the Cauchy problem

## TL;DR

This paper introduces a FEM-based numerical algorithm to accurately map EEG potentials from the scalp to the cortex by solving an ill-posed Cauchy problem, significantly enhancing EEG spatial resolution.

## Contribution

The paper presents a novel FEM-based approach for solving the Cauchy problem to improve EEG data mapping accuracy from scalp to cortex.

## Key findings

- Increases EEG spatial resolution to levels comparable with ECoG.
- Uses tetrahedral finite elements linear approximation for the solution.
- Provides an effective pre-processing algorithm for EEG data.

## Abstract

We propose an approach and the numerical algorithm for pre-processing of the electroencephalography (EEG) data, enabling to generate an accurate mapping of the potential from the measurement area - scalp - to the brain surface. The algorithm based on the solution of ill-posed Cauchy problem for the Laplace's equation using tetrahedral finite elements linear approximation. Application of the proposed algorithm sufficiently increases the spatial resolution of the EEG technique, making it comparable with much more complicated electrocorticography (ECoG) method.