Errors in Reprojection Methods in Computenzed Tomography

Iterative tomographic reconstruction methods have been developed which can enforce various physical constraints on the reconstructed image. An integral part of most of these methods is the repro. jection of the reconstructed image. These estimated projections are compared to the original projection data and modified according to some criteria based on a priori constraints. In this paper, the errors generated by such reprojection schemes are investigated. Bounds for these errors are derived under simple signal energy assumptions and using probabilistic assumptions on the distribution of discontinuities. These bounds can be used in the enforcement of constraints, in the determination of convergence of the iterative methods, and in the detection of artifacts.