X-ray computed tomography (CT) is a non-destructive technique for assessing the structural integrity of an object without compromising its usefulness. This imaging modality uses a number of projection measurements of the attenuated X-rays after passing through the object at different angles of incident beam orientation. The object is reconstructed from these projection measurement data usually using Filtered Backprojection (FBP) Algorithm which is based on Fourier Slice Theorem. FBP however assumes ideal conditions, notably monoenergetic X-ray photons and the availability of a very large number (hundreds and even thousands) of projections. However in practice, X-ray sources are polychromatic producing X-rays photons of varying energies and intensities. The X-ray attenuation of a material depends on energy, being high at low incident energy and decreasing as incident energy increases. This leads to an undesirable effect called beam hardening (BH). BH results in an underestimation of the attenuation values of the FBP reconstructed image, degrading it and thus potentially rendering it diagnostically unusable. In this thesis we propose a novel model-based correction scheme for BH based on the Lambert-Beer's law for polychromatic X-rays, knowledge of source spectrum and computer-aided design (CAD) model of the specimen. The validity of the correction scheme is demonstrated on a uniform tungsten alloy rod through simulation and experiment conducted using a 320 kVp X-ray source. It is found that the application of this correction scheme improves the beam hardened CT reconstructed image, particularly reducing the BH cupping artifact inherent in FBP reconstructed images. The proposed technique is evaluated using two quantitative metrics of the reconstructed image.The application of X-ray CT in the nuclear industry to inspect nuclear fuel rods is discussed in this thesis. For real-time tomography, data acquisition time is critical. In order to reduce the time for imaging there is a need to develop reconstruction algorithms using as few projections as possible. However limited number of projections implies an insufficiently filled Radon Space rendering imaging via FBP algorithm unsuitable. Any attempt to invert from the insufficiently filled Radon space back to the object space during the reconstruction problem gives rise to undesired artifacts which should be removed. In this thesis a novel artifact removal algorithm is proposed and its performance is demonstrated using both simulation and experimental data. A statistical reconstruction algorithm for reconstruction from a limited number of projections is also presented. The reconstruction results proves the technique to be promising in obtaining accurate inversion results, even in the presence of an extremely limited number of X-ray projections and noise. Availability of limited projections renders the X-ray CT problem ill-posed. In this thesis, X-ray CT problem is reformulated in terms of matrix product to facilitate the application of Tikhonov inversion technique. Reconstruction results obtained using a limited number of simulation and experimental data are shown and compared with FBP reconstructed results. It is relevant to note here that the new inversion technique is independent of any a priori information.
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