Invertibility and stability for a generic class of radon transforms with application to dynamic operators

Abstract

Abstract Let X be an open subset of {\mathbb{R}^{2}} . We study the dynamic operator, {\mathcal{A}} , integrating over a family of level curves in X when the object changes between the measurement. We use analytic microlocal analysis to determine which singularities can be recovered by the data-set. Our results show that not all singularities can be recovered as the object moves with a speed lower than the X-ray source. We establish stability estimates and prove that the injectivity and stability are of a generic set if the dynamic operator satisfies the visibility, no conjugate points, and local Bolker conditions. We also show this results can be implemented to fan beam geometry.