NUMERICAL-INTEGRATION OF THE RADON-TRANSFORM ON CLASSES E(S)(ALPHA) IN MULTIPLE (FINITE) DIMENSIONS

The reconstruction of functions from their projections calls for the (numerical) inversion of the Radon transform. Some of these methods, especially the filtered backprojection algorithms are of great importance in image reconstruction and also in computerized tomography. In this paper we consider a method for the reconstruction of sufficient smooth functions based on filtered backprojection by application of numbertheoretical numerical integration. For arbitrary finite dimensions we give a class of filter functions for the reconstruction and we establish error estimates and convergence rates for the numerical integration process. Further we present for the cases s = 2, 3 possible integration formulas for the filtered backprojection. Finally, we give some numerical reconstructions of the head phantom that confirm the theoretical results.