Quantitative Susceptibility Mapping Using Structural Feature Based Collaborative Reconstruction (SFCR) in the Human Brain

The reconstruction of MR quantitative susceptibility mapping (QSM) from local phase measurements is an ill posed inverse problem and different regularization strategies incorporating a priori information extracted from magnitude and phase images have been proposed. However, the anatomy observed in magnitude and phase images does not always coincide spatially with that in susceptibility maps, which could give erroneous estimation in the reconstructed susceptibility map. In this paper, we develop a structural feature based collaborative reconstruction (SFCR) method for QSM including both magnitude and susceptibility based information. The SFCR algorithm is composed of two consecutive steps corresponding to complementary reconstruction models, each with a structural feature based
$l 1$
norm constraint and a voxel fidelity based
$l 2$
norm constraint, which allows both the structure edges and tiny features to be recovered, whereas the noise and artifacts could be reduced. In the M-step, the initial susceptibility map is reconstructed by employing a
${\rm k} $
-space based compressed sensing model incorporating magnitude prior. In the S-step, the susceptibility map is fitted in spatial domain using weighted constraints derived from the initial susceptibility map from the M-step. Simulations and in vivo human experiments at 7T MRI show that the SFCR method provides high quality susceptibility maps with improved RMSE and MSSIM. Finally, the susceptibility values of deep gray matter are analyzed in multiple head positions, with the supine position most approximate to the gold standard COSMOS result.