An explicit method for the magnetoencephalography inverse problem based on data continuation

We have proposed a direct method for magnetoencephalography inverse problem in which the number, positions, and moments of the equivalent current dipoles (ECDs) are reconstructed algebraically. Although it can provide a good initial solution for the optimization-based iterative algorithms, the problem is that it requires the data on a closed surface which encloses the source. In this paper, we use the data continuation method proposed by Popov where the magnetic field at the missing sensor positions is extrapolated from the measured MEG data by solving linear boundary integral equations. After the data on a closed surface is obtained, ECDs are reconstructed using the direct method. The proposed method is verified with numerical simulations and PHANTOM experiments.