  Moment methods to reconstruct images from their Radon transforms are both
natural and useful. They can be used to suppress noise or other spurious
effects and can lead to highly efficient reconstructions from relatively few
projections. We establish a modified Radon transform (MRT) via convolution with
a mollifier and obtain its inversion formula. The relationship of the moments
of the Radon transform and the moments of its modified Radon transform is
derived and MRT data is used to provide a uniform approximation to the original
density function. The reconstruction algorithm is implemented, and a simple
density function is reconstructed from moments of its modified Radon transform.
Numerical convergence of this reconstruction is shown to agree with the derived
theoretical results.
