Tiny a priori knowledge solves the interior problem

Based on the Differentiated Backprojection (DBP) framework [1–3], 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 a more general uniqueness result which can be applied to a wider class of imaging configurations. The experimental results show evidence that the inversion corresponding to each obtained uniqueness result is stable.