An efficient mollifier method for three-dimensional vector tomography: convergence analysis and implementation

We consider the problem of three-dimensional vector tomography, that means the reconstruction of vector fields and their curl from line integrals over certain components of the field. It is well known that only the solenoidal part of the field can be recovered from these data. In this paper the method of approximate inverse is modified for vector fields and applied to this problem, leading to an efficient solver of filtered backprojection type. We prove convergence of the reconstructed solution, if the number of data tends to infinity, which means the method is exact. Finally, numerical results are presented for a straight flow through a cylinder.