Quantitative susceptibility map reconstruction via a total generalized variation regularization

Quantitative susceptibility mapping (QSM) is a last decade new concept which allows to determine the magnetic susceptibility distribution of tissue in-vivo. Nowadays it has several applications such as venous blood oxygenation and iron concentration quantification. To reconstruct high quality maps, a regularized scheme must be used to solve this ill-posed problem, due to the dipole kernel under sampling k-space. A widely used regularization penalty is Total Variation (TV), however, we can find stair casing artifacts in reconstructions due to the assumption that images are piecewise constant, not always true in MRI. In this sense, we propose a less restrictive functional, to avoid this problem and to improve QSM quality. A second order Total Generalized Variation (TGV) does not assume piecewise constancy in the images and is equivalent to TV in terms of edge preservation and noise removal. This work describes how TGV penalty addresses an increase in imaging efficiency in magnetic susceptibility maps from numerical phantom and in-vivo data. Currently, we report higher specificity with the proposed regularization. Moreover, the robustness of TGV suggest that is a possible alternative to tissue susceptibility mapping.