Towards an overall 3-D vector field reconstruction via discretization and a linear equations system

A tomographic method that efficiently reconstructs three-dimensional fields, despite the ill-posedness of recovering a vector field from line integrals, is presented in this paper. The analysis takes into consideration the methodology set forth in [1] for 2-D reconstruction and demonstrates that with the analogous discretization of the 3-D space and scanning lines, data redundancy is achieved and the solution is obtained from a linear equations system solution, using only information from finite boundary measurements. The adequacy of the method is illustrated by means of simulations on electrostatic fields. The motivation behind this work lies in its potential to bring forward an alternative brain mapping model from EEG recordings.