Azencott, Robert2018-12-032018-12-03August 2012016-08August 201Portions of this document appear in: Azencott, Robert, Bernhard G. Bodmann, Tasadduk Chowdhury, Demetrio Labate, Anando Sen, and Daniel Vera. "Region-of-Interest reconstruction from truncated cone-beam projections." arXiv preprint arXiv:1502.01114 (2015). And in: T. Chowdhury, A. Sen, and R. Azencott, "An iterative algorithm for region-of-interest reconstruction with cone-beam acquisitions on a generic source trajectory," in 13th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (Fully3D 2015), 2015.http://hdl.handle.net/10657/3608This 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.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. UH Libraries has secured permission to reproduce any and all previously published materials contained in the work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Computed tomographyCone-beam transformRadon transformInterior tomographyRegion-of-interest tomographyInverse problems2018-12-03Thesisborn digital