Acceleration d'une approche regularisee de reconstruction en tomographie a rayons X avec reduction des artefacts metalliques

This thesis is concerned with X-ray tomography of peripheral vessels that have undergone angioplasty with implantation of an endovascular metal stent. We seek to detect the onset of restenosis by measuring the lumen of the imaged blood vessel. This application requires the reconstruction of high-resolution images. In addition, the presence of a metal stent causes streak artifacts that complicate the lumen measurements in images obtained with the usual algorithms, like those implemented in clinical scanners.;As a first step, we consider the acceleration of a similar yet simpler algorithm, based on a monochromatic projection model. Since the reconstruction is reduced to the resolution of a nonlinear bound-constrained optimization problem, the reconstruction algorithm corresponds to an adequate numerical method for this problem. A fast method must be chosen according to an empirical comparison of numerical performance. This work contributes a stopping condition for numerical methods related to statistical properties of the reconstructed image, in order to establish the performance comparisons on equivalent images. This stopping condition is the basis to an original comparative analysis of tomography-specific numerical methods and general-usage optimization algorithms. It appears that these reach the stopping condition faster than a convergent tomography-specific method. This result justifies the adoption of the L-BFGS-B code for solving the reconstruction problem in the rest of the work.;A second significant advance was obtained by the decomposition of the image into the region of interest, a small area that contains the studied blood vessel, and the background, which contains the rest of the image. For known background, the reconstruction of the region of interest is very fast ; the background must thus be extracted from a fast preliminary (pilot) reconstruction of the full image. This full-image pilot can be obtained by one of two considered methods : an analytical approach or a coarse-grid regularized statistical algorithm. This thesis offers an original empirical comparison of these techniques for pilot reconstruction, based on image quality in the region of interest and total runtime. When the imaged object is composed of structures that cause strong reconstruction artifacts, it can be seen that using a statistical reconstruction procedure for the pilot leads to a better image quality in the region of interest than the analytical algorithm. However, short of such artifacts, the difference in region-of-interest quality between the two pilot approaches is insignificant. This comparison comes with a sensitivity analysis of the image quality in the region of interest to the pixel size of the background extracted from a statistical pilot reconstruction. It indicates that a relatively coarse background can be used without altering the image quality in the region of interest. This helps keeping the runtime short when the statistical approach is required.;Finally, we get back to the reconstruction based on a polychromatic projection model, which describes the beam hardening effect caused by the metal stent. Three innovative enhancements are brought to the model of De Man et al. (2001), in order to reduce the reconstruction runtime : 1. The decomposition of the image in background and region of interest, as described above ; 2. The coarse subsampling of the discrete model of the X-ray source emission spectrum, implemented by separately taking into account the contributions of the bremsstrahlung and of the characteristic emission to the X-ray beam ; 3. The gaussian modeling of the log-sinogram uncertainty, which leads to a regularized nonlinear least-squares reconstruction algorithm that is more robust to the data preprocessing computations performed during the acquisition. These enhancements reduce the reconstruction runtime by one order of magnitude. Moreover, the new algorithm proposed in this work offers a satisfactory compromise between image resolution and variance when the object is composed of larger metal structures.;A regularized statistical reconstruction algorithm, hinged on the maximization of the conditional log-likelihood of the image, is preferrable in this case. We choose a variant deduced from a data formation model that takes into account the nonlinear variation of X photon attenuation to photon energy, as well as the polychromatic character of the X-ray beam. This algorithm effectively reduces the artifacts specifically caused by the metal structures. Moreover, the algorithm may be set to determine a good compromise between image resolution and variance, according to data noise. This reconstruction method is thus known to yield images of excellent quality. However, the runtime to convergence is excessively long. The goal of this work is to reduce the reconstruction runtime.;In a nutshell, this thesis presents original comparative studies of numerical methods, object representation techniques and modeling strategies with respect to penalized-likelihood reconstruction. These studies lead to the implementation of various enhancements to the algorithm that significantly reduce the total computation time.