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

摘要

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