A discretized Fourier orthogonal expansion in orthogonal polynomials on a cylinder

Abstract

We study the convergence of a discretized Fourier orthogonal expansion in orthogonal polynomials on B 2 × [ − 1 , 1 ] , where B 2 is the closed unit disk in R 2 . The discretized expansion uses a finite set of Radon projections and provides an algorithm for reconstructing three-dimensional images in computed tomography. The Lebesgue constant is shown to be of asymptotic order m ( log ( m + 1 ) ) 2 , and convergence is established for functions in C 2 ( B 2 × [ − 1 , 1 ] ) .