Perfect Reconstruction of Classes of Non-Bandlimited Signals from Projections with Unknown Angles

In this paper, we consider the 2D tomography problem for a finite number of point sources, where the line integral projections are taken at unknown angles. We address the problem of recovering the point sources and estimating the projection angles. Using the property of the Radon transform of a point source, which is a signal with Finite Rate of Innovation, we retrieve the projections using the annihilating filter method. The reconstruction method we propose is then able to unveil the 2D geometric information of the projection angles, as well as the locations of the point sources. Finally, we extend the approach to planar polygons.