Using Tomography in Digital Plane to solve problems of Geometric Tomography.

In this talk we will study the problem of determining in a constructive way a convex body in the plane from its tomographic projections. For this, we consider the similar problem in digital plane: reconstructing a lattice convex set from its discrete tomographic projection. We show that we can use a reconstruction algorithm for the discrete problem to solve the continuous reconstruction to any precision. The proof of this result uses stability properties of geometric tomography. An extension to point-source tomographic projections is also investigated.