Florian Knoll1, Christian Clason2, Kristian Bredies2, Martin Uecker3, Rudolf Stollberger1
1Institute of Medical Engineering, Graz University of Technology, Graz, Austria; 2Institute for Mathematics & Scientific Computing, University of Graz, Graz, Austria; 3Biomedizinische NMR Forschungs GmbH, Max-Planck-Institut fuer biophysikalische Chemie, Goettingen, Germany
Nonlinear inversion was recently proposed for autocalibrated parallel imaging and shown to yield improved reconstruction quality. In addition, it has been shown that the aliasing arising from certain undersampled trajectories can be removed when using additional prior knowledge about the structure of the solution. Nonlinear inversion can be applied to arbitrary sampling trajectories, but the latter option was not yet exploited for this algorithm. In this work, it is demonstrated that nonlinear inversion can be extended with regularization terms that make use of such prior knowledge. The presented algorithms make use of the iteratively regularized Gauss-Newton method with additional variational constraints of total variation and total generalized variation type. Experimental results are presented for phantom and in-vivo measurements of undersampled radial and pseudorandom trajectories. The proposed approach yields results with reduced noise and undersampling artifacts in all cases when compared to conventional reconstruction with nonlinear inversion employing standard quadratic constraints.