Robust algorithms for discrete tomography

Tomography methods concentrate on reconstructing objects from multiple projections that are obtained by sending, for example, X-rays through the object. Applications of these methods are, among others, radiology (CT-, MRI- and PET scans), geophysics and material science. The tomographic problems can be formulated as a system of linear equations. Unfortunately, these systems are not symmetric nor positive (semi)definite, rank deficient and not square. In material science one is often presented with very small objects (like crystals or nano-structures) that consist of one or a small number of different materials, each with its own density. S