A sampling theorem for the Radon transform of finite complexity objects
We present sampling results for certain classes of 2-D signals that are not bandlimited, but have a parametric representation with a finite number of degrees of freedom, such as 2-D Diracs, polygons and bilevel signals with piecewise polynomial boundaries. As opposed to standard multidimensional sampling schemes, the proposed methods exploit the properties of the Radon transform of such signals. In particular, we demonstrate that by using an appropriate sampling kernel, one can perfectly reconstruct the signal from a finite set of samples of its Radon transform, and thus significantly reduce a computational load. The novel approach we present in the paper, offers practical algorithmic implementation and is potentially applicable to a large class of two-dimensional signals.