Three-dimensional reconstruction from few projections

This research project is concerned with iterative methods for tomographic reconstruction in problems where only very few projection data are available. A typical example of such a reconstruction problem is the 3D reconstruction of coronary arteries from rotational X-ray coronary angiography data. Due to the heart motion and the given acquisition parameters, typically only 5-10 projections are available for the reconstruction of each cardiac phase. The reconstruction therefore suffers from angular undersampling, the reconstruction problem is severely ill-posed. In order to obtain meaningful results from this very low number of projections, suitable regularizations for an iterative algorithm have to be found and to be implemented in an iterative reconstruction method. The reconstruction of coronary arteries is only one example of such a badly posed reconstruction problems. In a similar manner different regularizations and reconstruction algorithms have to be found, implemented, and tested for other badly-posed reconstruction problems.