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.