Weighted Group Lasso for a static EEG problem

TL;DR

This paper introduces a weighted Group Lasso method for static EEG source reconstruction, effectively reducing depth and orientation biases, with theoretical guarantees and practical strategies for improved neural activity localization.

Contribution

The paper proposes a novel weighted Group Lasso framework for EEG inverse problems, providing theoretical recovery guarantees and practical weighting strategies to enhance localization accuracy.

Findings

The method mitigates depth and orientation biases in EEG source localization.

Theoretical recovery guarantees are established for single and multiple sources.

Using a truncated Moore-Penrose pseudoinverse improves localization accuracy.

Abstract

We investigate the weighted Group Lasso formulation for the static inverse electroencephalography (EEG) problem, aiming at reconstructing the unknown underlying neuronal sources from voltage measurements on the scalp. By modelling the three orthogonal dipole components at each location as a single coherent group, we demonstrate that depth bias and orientation bias can be effectively mitigated through the proposed regularization framework. On the theoretical front, we provide concise recovery guarantees for both single and multiple group sources. Our numerical experiments highlight that while theoretical bounds hold for a broad range of weight definitions, the practical reconstruction quality, for cases not covered by the theory, depends significantly on the specific weighting strategy employed. Specifically, employing a truncated Moore-Penrose pseudoinverse for the involved weighting matrix gives a small Dipole Localization Error (DLE). The proposed method offers a robust approach for inverse EEG problems, enabling improved spatial accuracy and a more physiologically realistic reconstruction of neural activity.