FBP and the interior problem in 2D tomography

We consider the Filtered Back Projection reconstruction method in the case of interior data in Computerized Tomography. In this framework we prove that the difference between the FBP reconstruction and the measured function is a continuous function. This demonstrates that the FBP reconstruction contains the discontinuities of the measured image. Thus FBP can be considered as a local reconstruction method in CT. We show numerical experiments on both simulated and real data.