Structurally Constrained Quantitative Susceptibility Mapping

Introduction: Quantitative susceptibility mapping is a powerful technique that reveals changes in the underlying tissue susceptibility distribution. It is used to study a number of neuro-degenerative diseases since the susceptibility, , is highly correlated with the amount of iron deposition in the tissue (1). Reconstructing from the phase image collected with a gradient echo sequence is an ill-posed inverse problem due to the structure of the dipole kernel. Many approaches have been taken to overcome this difficulty including: thresholding the dipole kernel in the inversion process (TKD (2)), applying a geometrical constraint (iSWIM (3)), and utilizing multiple orientations to stabilize the inversion process (COSMOS (4)). Other studies try to use regularization techniques and different prior information such as structural constraints from magnitude images in the form of -norm (MEDI (5)), or from both magnitude and phase images in the form of -norm (HEIDI (6)). In (7), a structural constrained reconstruction (SFCR) method is proposed that is composed of two separate steps each includes both a fidelity term and two and -norm regularization terms. In the first step, the initial susceptibility map is reconstructed based on prior magnitude information. In the second step, the susceptibility map is fitted in the spatial domain using a weighted constraint derived from the initial map. The problems with the current QSM reconstruction algorithms are mainly related to the reliability of the geometry constraint and the speed of the reconstruction.