Constrained Tomography with Under-Sampled Projections

Inspection is central to maintaining the quality of products both during manufacturing and in storage. Non-destructive inspection of the internals of a product often requires imaging of the product by particles with low interaction cross section, such as X-rays. In Computed Tomography (CT), the 3D image is reconstructed using measurements of transmission using a large number of angles (projections), which takes a significant amount of time. This creates a challenge for the use of CT at scale. Certain features of the products are known, such as that the product is effectively made up of only a few materials. This knowledge can be included in the reconstruction as a constraint, which allows the 3D image to be reconstructed using a reduced set of projections. This Proposal builds on the novel binarity-constraint based reconstruction technique discovered by Drs. Markel and Levinson (Levinson, 2021) to propose the development of mathematical methods and computer software for constrained tomography with undersampled projections, which will enable inspection at scale.