An advanced dipole field inversion method for whole brain quantitative susceptibility mapping (QSM) without a traditional background field removal step, is proposed. To aid this ill-posed inversion process and obtain successful QSM, a Tikhonov regularization of the local susceptibility distribution is included. It is shown that the proposed method (Tikhonov-QSM) can substantially suppress reconstruction artefacts. More importantly, Tikhonov-QSM does not require edge erosion like in other QSM methods involving background field removal steps, preserving the cerebral cortex of the final images.
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