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Quantitative susceptibility mapping (QSM) is a recently developed MRI technique that provides a quantitative measure of tissue magnetic susceptibility. To compute tissue magnetic susceptibilities based on gradient echoes, QSM requires reliable unwrapping of the measured phase images and removal of contributions caused by background susceptibilities. Typically, the two steps are performed separately. Here, we present a method that simultaneously performs phase unwrapping and HARmonic (background) PhasE REmovaL using the LAplacian operator (HARPERELLA). Both numerical simulations and in vivo human brain images show that HARPERELLA effectively removes both phase wraps and background phase, whilst preserving all low spatial frequency components originating from brain tissues. When compared with other QSM phase preprocessing techniques, such as path-based phase unwrapping followed by background phase removal, HARPERELLA preserves the tissue phase signal in gray matter, white matter and cerebrospinal fluid with excellent robustness, providing a convenient and accurate solution for QSM. The proposed algorithm is provided, together with QSM and susceptibility tensor imaging (STI) tools, in a shared software package named 'STI Suite'.
Li et al. (Wed,) studied this question.