  Quantitative susceptibility mapping (QSM) utilizes MRI phase information to
estimate tissue magnetic susceptibility. The generation of QSM requires solving
ill-posed background field removal (BFR) and field-to-source inversion
problems. Because current QSM techniques struggle to generate reliable QSM in
clinical contexts, QSM clinical translation is greatly hindered. Recently, deep
learning (DL) approaches for QSM reconstruction have shown impressive
performance. Due to inherent non-existent ground-truth, these DL techniques use
either calculation of susceptibility through multiple orientation sampling
(COSMOS) maps or synthetic data for training, which are constrained by the
availability and accuracy of COSMOS maps or domain shift when training data and
testing data have different domains. To address these limitations, we propose a
weakly-supervised single-step QSM reconstruction method, denoted as wTFI, to
directly reconstruct QSM from the total field without BFR. wTFI uses the BFR
method RESHARP local fields as supervision to perform a multi-task learning of
local tissue fields and QSM, and is capable of recovering magnetic
susceptibility estimates near the edges of the brain where are eroded in
RESHARP and realize whole brain QSM estimation. Quantitative and qualitative
evaluation shows that wTFI can generate high-quality local field and
susceptibility maps in a variety of neuroimaging contexts.
