Sensitivity to error of the truncated Hilbert transform technique for interior reconstruction

Abstract

Historically, computed tomography reconstructions from truncated projection data have been considered non-unique. However, several recent results suggest that if the density of the object is known on some small region within the region of interest (ROI) then a unique and stable reconstruction of the complete ROI may be possible. Unfortunately, prior knowledge of the exact density of an object being scanned is uncommon, and as such an experimentally determined estimate must be used in its place. This estimate will naturally contain errors. We have performed several reconstruction simulations to establish the sensitivity of the proposed algorithm to errors in the prior knowledge. Our results suggest that the most important element of the prior knowledge is its mean value, while perturbations of the details cause fewer problems in the reconstructed images.