2015/02/04 by Robert Azencott, Azencott, Robert, Bernhard G. Bodmann +9
Engineering · Medicine · #Advanced X-ray and CT Imaging #FOS: Physical sciences #Mathematical Physics (math-ph) #Medical Imaging Techniques and Applications #Radiation Dose and Imaging
paper · pdf · doi:10.48550/arxiv.1502.01114
openalex publication_date 2015/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Region-of-Interest (ROI) tomography aims at reconstructing a region of interest C inside a body using only x-ray projections intersecting C with the goal to reduce overall radiation exposure when only a small specific region of the body needs to be examined. We consider x-ray acquisition from sources located on a smooth curve Γ in ℝ3 verifying classical Tuy's condition. In this situation, the \it non-trucated cone-beam transform D f of smooth densities f admits an explicit inverse Z; however Z cannot directly reconstruct f from ROI-truncated projections. To deal with the ROI tomography problem, we introduce a novel reconstruction approach. For densities f in L∞(B) where B is a bounded ball in ℝ3, our method iterates an operator U combining ROI-truncated projections, inversion by the operator Z and appropriate regularization operators. Assuming only knowledge of projections corresponding to a spherical ROI C ⊂ B, given ε>0, we prove that if C is sufficiently large our iterative reconstruction algorithm converges uniformly to an ε-accurate approximation of f, where the accuracy depends on the regularity of f quantified in the Sobolev norm W5(B). This result shows the existence of a critical ROI radius ensuring the convergence of the ROI reconstruction algorithm to ε-accurate approximations of f. We numerically verified these theoretical results using simulated acquisition of ROI-truncated cone-beam projection data for multiple acquisition geometries. Numerical experiments indicate that the critical ROI radius is fairly small with respect to the support region~B.