Reconstruction of vector fields in bounded domain vector tomography

This paper considers the problem of vector tomography on an arbitrary bounded domain in three dimensions. Previous work has given the formulas for the reconstructed scalar and vector potential functions in relation to the vector field values inside the domain and on the boundary of the domain. Using these formulas. It is shown that the curl-free component can be reconstructed using only one probe measurement, and the divergence-free component can be reconstructed using only two probe measurements. No boundary measurements are necessary