Titre de la thèse: Bayesian Multi-Energy Computed Tomography reconstruction approaches based on decomposition models
Résumé de la thèse: Compared to classical Computed Tomography (CT), Multi-Energy Computed Tomography (MECT) is able to provide more information about the object. One of its interests is to get several separate images of basis materials. Water and bone are two commonly used basis materials in medical applications. MECT shows great potentials in medical diagnostic applications and other non-destructive testing applications, like luggage inspection, explosive detection etc. However, existing reconstruction approaches are either have low reconstruction accuracy or very sensitive to noise. Another difficulty in MECT reconstruction is to taking into account of the beam polychromaticity. The X-ray beams generated by an ordinary tube cover a broad band of energies. This indicates that the true forward model which describes the relation between the observation and the unknown object parameter is non-linear. The commonly used negative-log linearization causes Beam-Hardening Artifacts (BHA). The major objective of this work is to develop high quality MECT reconstruction approaches which can overcome these difficulties. The first contribution of our work is to propose a Bayesian MECT reconstruction approach for monochromatic MECT where the beam polychromaticity is ignorable but the measurements at different have variant SNRs. This corresponds to the MECT system realized by using an energy-resolving detector. In order to make the projection data could contain as much information as possible, we have conducted a theoretic study on optimal energy choices in terms of minimizing the basis material separation conditioning. The result shows that dual-energy measurements are sufficient enough to reconstruct the water and bone images. Measurements at a third energy are required only in situations where the object contains heavy materials, like iodine. After that, we have proposed a Bayesian reconstruction approach based on a Gaussian noise model and Huber prior model. By using a pre-estimated noise covariance matrix from direct measurements, the proposed approach is able to take into account of the variant SNRs. The performance is analyzed based on numerical simulations. The result shows that it is more robust to noise and have higher reconstruction accuracy compared the existing analytical approaches. The second contribution of our work is to propose a full-spectral MECT reconstruction approach which could take into account of the beam polychromaticity and be used in more general MECT configurations. For this objective, we have proposed a Bayesian reconstruction approach based on the exact non-linear forward model and a Gaussian noise model with unknown variances. The major difference of our work compared to the literature is the joint estimation of the noises and the basis material decomposition fractions. By referring to the joint MAP estimation method and the Dirac prior model assigned to the variances, we have successfully transformed the joint reconstruction problem into an optimization problem, which is solved later by using a non-linear Conjugate-Gradient (CG) algorithm. The performance of the proposed approach is analyzed with both simulated and experimental data. The result shows that it is robust to noise and material. Compared to existing analytical approaches, it has advantages in noise robustness; compared to linearized statistical approaches, it has higher separation accuracy and less BHA.