Image reconstruction from fan-beam and cone-beam projections

This thesis addresses the problem of reconstructing static objects in 2D and 3D transmission computed tomography (CT). After reviewing the classical CT reconstruction theory, we discuss and thoroughly evaluate various novel reconstruction methods, two of which are original. Our first original approach is for 2D CT reconstruction from full-scan fan-beam data, i.e., for 2D imaging in the geometry of diagnostic medical CT scanners. Compared to conventional methods, our approach is computationally more efficient and also yields results with an overall reduction of image noise at comparable spatial resolution, as demonstrated in detailed evaluations based on simulated fan-beam data and on data collected with a Siemens Somatom CT scanner. Part two of this thesis discusses the problem of 3D reconstruction in the short-scan circular cone-beam (CB) geometry, i.e., the geometry of medical C-arm systems. We first present a detailed comparative evaluation of innovative methods recently suggested in the literature for reconstruction in this geometry and of the approach applied on many existing systems. This evaluation involves various quantitative and qualitative figures-of-merit to assess image quality. We then derive an original short-scan CB reconstruction method that is based on a novel, theoretically-exact factorization of the 3D reconstruction problem into a set of independent 2D inversion problems, each of which is solved iteratively and yields the object density on a single plane. In contrast to the state-of-the-art methods discussed earlier in this thesis, our factorization approach does not involve any geometric approximations during its derivation and enforces all reconstructed values to be positive; it thus provides quantitatively very accurate results and effectively reduces CB artifacts in the reconstructions, as illustrated in the numerical evaluations based on computer-simulated CB data and also real CB data acquired with a Siemens Axiom Artis C-arm system.