This paper presents a new method for tomographic reconstruction of volumes from sparse observational data. Application scenarios can be found in astrophysics, plasma physics, or whenever the amount of obtainable measurement is limited. In the extreme only a single view of the phenomenon may be available. Our method uses input image data together with complex, user-definable assumptions about 3D density distributions. The parameter values of the user-defined model are fitted to the input image. This allows for incorporating complex, data-driven assumptions, such as helical symmetry, into the reconstruction process. We present two different sparsity-based reconstruction approaches. For the first method, novel virtual views are generated prior to tomography reconstruction. In the second method, voxel groups of similar target densities are defined and used for group sparsity reconstruction. We evaluate our method on real data of a high-energy plasma experiment and show that the reconstruction is consistent with the available measurement and 3D density assumptions. An additional experiment on simulated data demonstrates possible gains when adding an additional view to the presented reconstruction methods.
We introduce a new algorithm to reduce metal artifacts in computed tomography images when data is acquired using a single source spectrum. Our algorithm is a hybrid approach which corrects the sinogram vector followed by an iterative reconstruction. Many prior sinogram correction algorithms identify projection measurements that travel through areas with significant metal content, and remove those projections, interpolating their values for use in subsequent reconstruction. In contrast, our algorithm retains the information of random subsets of these metal-affected projection measurements, and uses an average procedure to construct a modified sinogram. To reduce the secondary artifacts created by this interpolation, we apply an iterative reconstruction in which the solution is regularized using a sparsifying transform. We evaluate our algorithm on simulated data as well as data collected using a medical scanner. Our experiments indicate that our algorithm reduces the extent of metal artifacts significantly, and enables accurate recovery of structures in proximity to metal.