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 E denote the operator, which corresponds to the error term of an inversion formula. It is proven that in both cases E: H0m→H0m+1 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 E 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