Fast, large scale optimization algorithms for tomographic image reconstruction.

Tomography imaging techniques produce volumetric images of the three-dimensional structure of an object. X-ray radiation is one of the standard modalities used for threedimensional imaging and in this case, X-ray projection images are typically collected from the object at different orientations. These projections are then used to compute a volumetric representation of the object’s internal x ray attenuation profile. Scientific and industrial tomographic imaging applications require the use of ever more massive datasets as they increasingly use larger and higher resolution detectors and use increasing numbers of projections to scan the object with the required resolution. Furthermore, the need to discern ever-finer details within an object leads to an increase in the desired resolution of the reconstructed volume. If this is paired with the usage of non-standard tomographic scanning trajectories, then the filtered back-projection algorithm, which remains the primary workhorse for the tomographic reconstruction of large datasets, is no longer applicable. Compared to back projection based methods, iterative algorithms have many advantages for linear tomographic image reconstruction. However, for largescale tomographic reconstruction using computation nodes with limited storage capacity, the projection data and the reconstructed image vector have to be both partitioned into many smaller blocks. Each iteration in a traditional iterative method needs access to either all projection data or to the entire image (or to both) and thus needs to iterate over individual blocks that need to be copied to the processing node. This additional data access can significantly reduce reconstruction speed. To address these challenges, this project develops novel algorithms that are tailored to large-scale tomographic reconstruction. The algorithms are designed to fit on modern high-performance computing infrastructures, where each computation node does not have fast access to the entire dataset at once and where communication between different nodes is relatively slow. This thesis includes the introduction of the developed algorithms, the comparison of them with existing methods and the application of them on realistic parallel network