Region-of-Interest Reconstruction from Truncated Cone-Beam CT

This thesis presents a novel algorithm in 3D computed tomography (CT) dedicated to accurate region of interest (ROI) reconstruction from truncated cone-beam projections. Here data acquisition involves cone-beam x-ray sources positioned on any piecewise smooth 3D-curve satisfying the very generic, classical Tuy's conditions and uses only x-rays passing through the ROI. Our ROI-reconstruction algorithm implements an iterative procedure where we systematically alternate intermediary reconstructions by an exact non-truncated cone-beam inversion operator, with an effective density regularization method. We validate the accuracy of our ROI-reconstruction algorithm for a 3D Shepp-Logan phantom, a 3D image of a Mouse, and a 3D image of a human jaw, for different cone-beam acquisition curves, including the twin-orthogonal circles and the spherical spiral curve, by simulating ROI-censored cone-beam data and our iterative ROI-reconstruction for a family of spherical ROIs of various radii. The main result is that, provided the density function is sufficiently regular and the ROI radius is larger than a critical radius, our procedure converges to an $\epsilon$-accurate reconstruction of the density function within the ROI. Our extensive numerical experiments compute the critical radius for various accuracy levels $\epsilon$. These results indicate that our ROI reconstruction is a promising step towards addressing the dose-reduction problem in CT imaging.Mathematics, Department o