Discrete projection: Highly correlated arrays and ghosts for image reconstruction

Tomography studies the reconstruction of images from projected observations made at various angles. This thesis focuses explicitly on discrete projections, which sum only points across a regular finite grid that intersect straight lines. Discrete projection methods are used in this thesis to assemble highly structured arrays where individual points are purposefully positioned to amplify or reduce the spatial correlations between neighbourhoods, or as tilings with shapes that leave tomographic projections unchanged. These arrays find use in imaging, communication technology, online security, crystallography and material science. Algorithms are provided to perform these tasks efficiently.