An accurate approximate algorithm for motion compensation in two-dimensional tomography
Abbreviated Journal Title
GENERALIZED RADON-TRANSFORM; RECONSTRUCTION; PLANE; FIELD; Mathematics, Applied; Physics, Mathematical
In this paper, we propose two approximate inversion formulae for motion compensation in tomography: for parallel beam and fan beam geometries. Let epsilon denote the operator, which corresponds to the error term of an inversion formula. It is proven that in both cases epsilon : H(0)(m) -> H(0)(m+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 epsilon 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.
"An accurate approximate algorithm for motion compensation in two-dimensional tomography" (2010). Faculty Bibliography 2010s. 339.