Differentiable Procedures for Optimization in Computed Tomography Reconstruction
Computed Tomography (CT) is used across disease diagnosis, treatment planning, intra-operative guidance, and research, but the images it produces can be marred by artifacts whenever real-world effects disrupt the measurement process without being accounted for during reconstruction. This thesis extends the standard CT reconstruction pipeline with correction modules that explicitly model these disruptive effects and are optimized directly from the acquired projection data, following two guiding principles throughout: developing informative target functions to judge image quality, and using end-to-end gradient-based optimization to update the correction parameters.
For the target functions, the thesis explores a range of options: from classic total variation, to trained networks that estimate reference-based quality metrics without needing an actual reference image, to a fully reference-free approach that judges quality by how likely an image is to be artifact-free. Because these functions are defined in the image domain while the parameters being optimized often act earlier, before or during backprojection, the thesis pairs automatic differentiation with specially built differentiable backprojection operators to connect the two.
The first contribution applies this approach to cupping artifacts, estimating correction coefficients for a sinogram-space adjustment function, and shows this effectively removes the artifact in a dataset of murine bone scans. The second line of work tackles patient motion, a major source of artifacts, focusing on head imaging. Here, an analytical method translates gradient information from the reconstructed image back into the geometry of the backprojection operator, converting an entire class of motion-correction algorithms into a gradient-based optimization setting. Tested across several head CT datasets, including both simulated and real clinical cone-beam CT scans, this approach achieves a 19-fold speedup along with better motion compensation than existing methods.
Across both applications, combining an analytical solution to the underlying inverse problem with gradient-based optimization of image-domain correction modules proved to be a powerful, general principle, one the thesis suggests should extend to other artifacts and potentially beyond CT reconstruction entirely.