  We study the convergence of a discretized Fourier orthogonal expansion in
orthogonal polynomials on $B^2 \times [-1,1]$, where $B^2$ is the closed unit
disk in $\RR^2$. 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 $m \,
(\log(m+1))^2$, and convergence is established for functions in $C^2(B^2 \times
[-1,1])$.
