Radon Transform Theory for Random Fields and Optimum Image Reconstruction from Noisy Projections

Abstract

Reconstruction from Noisy Projections/ In this chapter we present some recent results on Radon transform theory for stationary random fields. Specifically, we present a 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 multi-dimensional spectral estimation from one-dimensional projections, noise analysis in computed tomography, etc.