Model-based image reconstruction in X-ray computed tomography

The thesis investigates the applications of iterative, statistical reconstruction (SR) algorithms in X-ray Computed Tomography. Emphasis is put on various aspects of system modeling in statistical reconstruction. Fundamental issues such as effects of object discretization and algorithm initialization on reconstructed images are thoroughly investigated. We show that artifacts may emerge in reconstructions if overly coarse image grids are used. Only by reconstructing on a finer grid than would be used in analytical algorithms one can retain the main advantage of SR over analytical methods: the improved resolution-noise trade-off. Furthermore, we demonstrate that the emergence of the abovementioned artifacts is more related to the density of object discretization than to the selection of image basis function: for coarse grids, artifacts emerge both for voxel- and blob-based image representations. Another important finding is that the use of an analytically reconstructed image as initial guess for SR may result in significant acceleration of SR's convergence around small, high-contrast structures. Speed-ups of up to one order of magnitude are achievable. The noise injected with this analytically computed initial estimate is promptly removed by SR, so the acceleration is obtained without any penalty in terms of resolution-noise trade-off. The thesis demonstrates also how the use of system modeling during reconstruction improves the quality of X-ray CT images. We introduce an efficient and accurate Monte Carlo-based scheme for the correction of scatter-induced image artifacts. To this end, a dedicated Monte Carlo (MC) simulator of X-ray CT scanners is developed. With the simulator, the scale of scatter-induced artifacts is investigated for the case of micro-CT imaging. It is found that scatter is responsible for as much as 50% of the strength of cupping artifacts present in the reconstructions of rat-sized objects. The proposed MC simulator uses an advanced fitting scheme to significantly reduce the computational time needed to obtain an accurate estimate of object scatter. Acceleration factors of three-four orders of magnitude are attainable. Such a rapid scatter simulation is no longer a computational bottleneck during image reconstruction. When the accelerated MC simulator is combined with poly-energetic statistical reconstruction algorithm, micro-CT images almost free of any scatter or beam hardening artifacts are achieved. Strong reduction of artifacts is attained both for real and simulated micro-CT data. Furthermore, we investigate a micro-CT configuration based on arrays of modular detectors. In such a design, appearance of gaps between the modules seems inevitable. We show that by using SR one may obtain volumetric reconstructions free of any gap-induced artifacts even for systems where discontinuities cover as much as 10% of detector area. It has only to be ascertained that the projection data collected with the modular detector is complete in the central imaging plane. An important advantage of SR is that no pre-processing of non-continuous projections is required in order to arrive at an artifact free image. These findings may also be applicable to the case of malfunctioning detector cells in conventional CT systems