Florian Knoll1, Kristian Bredies2, Thomas Pock3, Rudolf Stollberger1
1Institute of Medical Engineering, Graz University of Technology, Graz, Austria; 2Institute for Mathematics and Scientific Computing, University of Graz, Graz, Austria; 3Institute for Computer Graphics and Vision, Graz University of Technology, Austria
Total Variation was recently introduced in many different MRI applications. The assumption of TV is that images consist of areas which are piecewise constant. However, in many practical MRI situations, this assumption is not valid due to the existence of smooth signal inhomogeneities originating from the exiting b1 field or the receive coils. This work introduces the new concept of Total Generalized Variation for MRI, a new mathematical framework which is a generalization of the TV theory and which eliminates these restrictions. Two important applications are considered in this paper, image denoising and iterative image reconstruction from undersampled radial data sets with multiple coils. Apart from simulations, experimental results from in vivo measurements are presented where TGV yielded improved image quality over conventional TV in all cases.