Reconstruction from Radon projections and orthogonal expansion on a ball

The relation between Radon transform and orthogonal expansions of a function on the unit ball in \RR^d is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to algorithms for image reconstruction from Radon data. The relation between orthogonal expansion and the singular value decomposition of the Radon transform is also exploited.Comment: 15 page

Cubature Formulae and Orthogonal Polynomials

The connection between orthogonal polynomials and cubature formulae for the approximation of multivariate integrals has been studied for about 100 years. The article J. Radon published about 50 years ago has been very inuential. In this text we describe some of the results that were obtained during the search for answers to questions raised by his article