Density Reconstruction Using Arbitrary Ray Sampling Schemes

Abstract

Methods for calculating the distribution of absorption densities in a cross section through an object from density integrals along rays in the plane of the cross section are well known, but are restricted to particular geometries of data collection. So-called convolutional-backprojection-summation methods, used now for parallel ray data, have recently been extended to special cases of the fan-beam reconstruction problem by the addition of pre- and post-multiplication steps. In this paper, I present a technique for deriving reconstructing algorithms for arbitrary ray-sampling schemes: the resulting algorithms entail the use of a general linear operator, but require little more computation than the convolutional methods, which represent special cases.