Localization of active neural source (ANS) from measurements on head surface is vital in magnetoencephalography. As neuron-generated magnetic fields are extremely weak, significant uncertainties caused by stochastic measurement interference complicate its localization. This paper presents a novel computational method based on reconstructed magnetic field from sparse noisy measurements for enhanced ANS localization by suppressing effects of unrelated noise. In this approach, the magnetic flux density (MFD) in the nearby current-free space outside the head is reconstructed from measurements through formulating the infinite series solution of the Laplace's equation, where boundary condition (BC) integrals over the entire measurements provide "smooth" reconstructed MFD with the decrease in unrelated noise. Using a gradient-based method, reconstructed MFDs with good fidelity are selected for enhanced ANS localization. The reconstruction model, spatial interpolation of BC, parametric equivalent current dipole-based inverse estimation algorithm using reconstruction, and gradient-based selection are detailed and validated. The influences of various source depths and measurement signal-to-noise ratio levels on the estimated ANS location are analyzed numerically and compared with a traditional method (where measurements are directly used), and it was demonstrated that gradient-selected high-fidelity reconstructed data can effectively improve the accuracy of ANS localization.
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