Thies M (2025)
Publication Language: English
Publication Type: Thesis
Publication year: 2025
URI: https://open.fau.de/handle/openfau/37148
Computed Tomography (CT) is utilized in diverse applications, particularly in disease diagnosis, treatment, intra-operative guidance, as well as clinical and preclinical research. However, artifacts can emerge when different effects disrupt the measurement process and are not addressed in the reconstruction of interpretable images from measured data. In this thesis, the analytic CT reconstruction pipeline is enhanced with correction modules that reduce specific artifacts by explicitly modeling the underlying effects and that are optimized using only the acquired projection data. All contributions in this thesis follow two key design principles. First, to exploit optimization methods, informative target functions must be developed. Various image-domain functions are proposed, from total variation over trained networks that estimate reference-based metrics without references to a completely reference-free approach utilizing the likelihood of being artifact-free as a surrogate metric. These functions assess the quality of a reconstructed image, guiding optimization. Second, an end-to-end gradient-based optimization approach is employed for parameter updates. While the target function is formulated in the image domain, parameters often influence the reconstruction process before or during the backprojection step. Thus, our methods are based on automatic differentiation paired with specialized differentiable backprojection operators. This work’s first contribution estimates the coefficients of a function for adjusting line integral values in sinogram space to reduce cupping artifacts. Employing the mentioned design principle – an image-domain target function with end-to-end gradient-based optimization – effectively compensates for this effect, as demonstrated in a data set of murine bones. A second line of contributions addresses patient motion, which can create significant artifacts in reconstructed images. Focusing on head anatomy, the rigid motion patterns underlying a given scan need to be estimated such that a corrected image can be obtained from a motion-compensated reconstruction. An analytical method is developed to translate gradient information from the reconstructed image into the backprojection operator’s geometry. This approach, integrated into the optimization pipeline, enables the conversion of a full class of algorithms into a gradient-based setting, significantly accelerating optimization over current methods. On multiple head CT data sets, including simulated and real clinical cone-beam CT measurements, we attain a 19-fold speed-up as well as superior motion compensation performance compared to existing methods. Incorporating the analytical solution to the inverse problem into a gradient-based optimization pipeline and optimizing integrated correction modules using an image-domain objective function has proven a powerful principle for the mentioned applications. We are confident that this idea also extends to other artifacts and even beyond the realm of CT reconstruction.
APA:
Thies, M. (2025). Differentiable Procedures for Optimization in Computed Tomography Reconstruction (Dissertation).
MLA:
Thies, Mareike. Differentiable Procedures for Optimization in Computed Tomography Reconstruction. Dissertation, 2025.
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