The approximate inverse in action III: 3D-Doppler tomography

The approximate inverse is a powerful tool for solving first kind operator equations in a stable way. Its abstract convergence and stability theory developed in our articles [SIAM J. Numer. Anal., 37, 1909-1929,2000] and [Math. Comp., 72, 1399-1415, 2003] is applied to the reconstruction problem of 3D-vector field tomography resulting in a reconstruction algorithm of filtered backprojection type. For an analytically computed reconstruction filter (reconstruction kernel) convergence with rates as well as the regularization property are established.