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Quantitative susceptibility mapping (QSM) is a novel magnetic resonance-based technique that determines tissue magnetic susceptibility from measurements of the magnetic field perturbation. Due to the ill-posed nature of this problem, regularization strategies are generally required to reduce streaking artifacts on the computed maps. The present study introduces a new algorithm for calculating the susceptibility distribution utilizing a priori information on its regional homogeneity derived from gradient echo phase images and analyzes the impact of erroneous a priori information on susceptibility map fidelity. The algorithm, Homogeneity Enabled Incremental Dipole Inversion (HEIDI), was investigated with a special focus on the reconstruction of subtle susceptibility variations in a numerical model and in volunteer data and was compared with two recently published approaches, Thresholded K-space Division (TKD …