Super-resolution for MEG Inversion -Reconstruction from the Partial Boundary Measurement

Magnetoencephalography (MEG) is a measurement technique of the magnetic field outside the human brain, from which neural activities inside the brain are estimated. So far, we have proposed a direct method where the locations and moments of the equivalent current dipoles modeling the synchronous and focal neural activities are explicitly represented by the magnetic field on the closed surface which encloses the human brain. In this paper, we extend it to the case where the data is restricted on the partial boundary such as an upper hemisphere in the practical MEG. We use the super-resolution technique, which has been originally proposed for reconstruction of a function with a bounded support and missing spectral components. First, we estimate ECDs by the direct method using the data on the upper hemisphere only assuming that the data on the lower hemisphere which lacks the sensors to be zero. Second, using the estimated ECD parameters, we compute the magnetic field on the lower hemisphere. From the measured/computed data on the upper/lower hemisphere, the magnetic field on the closed surface is obtained. Then, we re-estimate ECDs using the direct method and repeat these processes. Convergence proof can be conducted using convex projections. Numerical experiments show that localization accuracy is sufficiently improved