MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Efficient Computation of Lead Field Bases and Influence Matrix for the FEM-based EEG and MEG Inverse Problem. Part I: Complexity Considerations

Carsten H. Wolters, Lars Grasedyck and Wolfgang Hackbusch


The inverse problem in Electro- and Magneto-EncephaloGraphy (EEG/ MEG) aims at reconstructing the underlying current distribution in the human brain using potential differences and/or magnetic fluxes that are measured non-invasively directly, or at a close distance, from the head surface. The simulation of EEG and MEG fields for a given dipolar source in the brain using a volume-conduction model of the head is called the forward problem. The Finite Element (FE) method, used for the forward problem, is able to realistically model tissue conductivity inhomogeneities and anisotropies, which is crucial for an accurate reconstruction of the current distribution. So far, the computational complexity is quite large when using the necessary high resolution FE models.

In this paper we will derive algorithms for the efficient computation of EEG and MEG lead fields bases which exploit the fact that the number of sensors is generally much smaller than the number of reasonable dipolar sources.

The state-of-the-art forward approach will be speeded up by a factor of more than 100 for a realistic choice of the number of sensors and sources.

Our approaches can be applied to inverse reconstruction algorithms in both continuous and discrete source parameter space for EEG and MEG. In combination with algebraic multigrid solvers, the presented approach leads to a highly efficient solution of FE-based source reconstruction problems.

eeg/meg, algebraic multigrid method, source reconstruction, conductivity anisotropy and inhomogeneity, finite element method, inverse method, reciprocity, hierarchical matrices

Related publications

2004 Repository Open Access
Carsten H. Wolters, Lars Grasedyck and Wolfgang Hackbusch

Efficient computation of lead field bases and influence matrix for the FEM-based EEG and MEG inverse problem

In: Inverse problems, 20 (2004) 4, pp. 1099-1116