Marius Nitzsche

Dynamic Inverse Problems in Imaging

If the examined object moves during data acquisition - for instance a breathing patient in Computed Tomography (CT) or Magnetic Particle Imaging (MPI) - the assumed forward operator no longer matches the measured data, causing artifacts on which classical methods fail. The usual approach is to measure the motion or estimate it at considerable cost. The algorithms I work on do exactly the opposite: the motion is never determined explicitly, but treated as an unknown model inexactness of which only error bounds are known. Based on iterative methods, this yields reconstructions that remain provably stable even though the exact operator is never known.

Unsupervised Deep Learning for Image Reconstruction

Neural networks can improve image reconstruction considerably, but classically require large training sets with reference images - which are often unavailable in practice, especially in the dynamic case. I investigate approaches that work without any reference data: the network is trained directly on the measured data and combined with classical variational methods. Here, too, motion and other model deviations are neither measured nor reconstructed explicitly, but compensated implicitly during reconstruction.