| Currently, most images in clinical computed tomography (CT) are generated from measurements of attenuated X-ray intensities using an analytical backprojection method, such as filtered backprojection (FBP). In addition to ignoring other physical effects, these methods generally ignore geometric factors such as integrations over the finite focal spot and finite detector.;The ability to model system parameters is a potential advantage of iterative reconstruction (IR). However, the importance of modeling system geometry in IR has been unclear. When geometry is modeled, it is usually modeled with linearized line integrals given by log-processed data. However, any linear modeling of finite source and detector effects in the log domain is necessarily approximate, since these finite apertures lead to linear averaging in the transmitted intensity domain, not in the log-processed domain of line integrals. In this dissertation, we develop an IR method that is able to model system geometry using both averaging over X-ray intensities and over linearized line integrals. We use this method to compare image reconstructions with no geometric modeling to those with modeling. We determine that while geometric modeling may be important, especially at the periphery of an image, modeling in the transmitted intensity domain may not be worth its increased computational cost.;While forms of IR are becoming an option on clinical scanners, wide implementation of IR has been slow due to high computational costs and reconstruction times longer than analytical methods. Previous work by our group has utilized penalized-likelihood sinogram restoration, which for two-dimensional (2D) geometries has been shown to reduce noise and to correct for geometric effects and other degradations at a lower computational cost than fully iterative image reconstruction. In addition to focusing on 2D, previous work in sinogram restoration used a quadratic smoothing penalty. In this dissertation, we introduce a sinogram restoration update equation for non-quadratic penalties, allowing for the use of the edge-preserving Huber penalty, which shows improvements in resolution-variance properties compared to the quadratic penalty. We also expand sinogram restoration with corrections for degradations to the clinically relevant helical cone-beam geometry, showing the feasibility of sinogram restoration for clinical data. |
