Radon and Mojette Projections’ Equivalence for Tomographic Reconstruction using Linear Systems

Abstract

In medical imaging, the Radon transform, used for tomographic reconstruction, recovers a N-Dimensional image from a set of acquired (N-1)D projections. However, it implies approximations in discrete domain. Beside this transform, Mojette transform has been developped as a discrete and exact transform. However, its construction is incompatible with physical X-Rays properties. In this paper, after having recalled generalities about both transforms, we introduce the conditions under which their projections are equivalent and how to reconstruct an image with the Mojette backprojection from a Radon acquisition using linear systems. This method will be applied on some examples and results will be compared with usual Radon transform.