An accurate approximate algorithm for motion compensation in two-dimensional tomography^*

In this paper, we propose two approximate inversion formulae for motion compensation in tomography: for parallel beam and fan beam geometries. Let denote the operator, which corresponds to the error term of an inversion formula. It is proven that in both cases is bounded; thus, the error term is one order smoother than the original function f in the scale of Sobolev spaces. It is also proven that in both cases if the motion map approaches the identity map, then the norm of approaches zero. The formulae can be easily implemented numerically. Results of numerical experiments in the fan-beam case (which is more common in applications) demonstrate good image quality even when motion is relatively strong.