Radon transform theory for random fields and optimum image reconstruction from noisy projections

In this paper we present some new results on Radon transform theory for stationary random fields. In particular we present a new projection theorem which gives the relation between the power spectrum density of one dimensional projections of a stationary random field and its two dimensional power spectrum density. This result yields the optimum mean square reconstruction filter from noisy projections and is useful in other problems such as multidimensional spectral estimation from one dimensional projections, noise analysis in computed tomography, etc. Example are given to demonstrate the usefulness of these results.