Tinya prioriknowledge solves the interior problem in computed tomography

Abstract

Based on the concept of Differentiated Backprojection (DBP) (Noo et al 2004 Phys.Med.Biol. 49 3903-3923, Pan et al 2005 Med.Phys. 32 673-684, Defrise et al 2006 Inverse Problems 22 1037-1053), this paper shows that the solution to the interior problem in computed tomography is unique if a tiny a priori knowledge on the object f(x,y) is available in the form that f(x,y) is known on a small region located inside the region of interest. Furthermore, we advance the uniqueness result to obtain more general uniqueness results which can be applied to a wider class of imaging configurations. We also develop a reconstruction algorithm which can be considered an extension of the DBP-POCS (Projection Onto Convex Sets) method described by Defrise et al (2006 Inverse Problems 22 1037-1053), where we not only extend this method to the interior problem but also introduce a new POCS algorithm to reduce computational cost. Finally, we present experimental results which show evidence that the inversion corresponding to each obtained uniqueness result is stable.