Nonlinear Dipole Inversion (NDI) enables Quantitative Susceptibility Mapping (QSM) without parameter tuning

We propose Nonlinear Dipole Inversion (NDI) for high-quality Quantitative\nSusceptibility Mapping (QSM) without regularization tuning, while matching the\nimage quality of state-of-the-art reconstruction techniques. In addition to\navoiding over-smoothing that these techniques often suffer from, we also\nobviate the need for parameter selection. NDI is flexible enough to allow for\nreconstruction from an arbitrary number of head orientations, and outperforms\nCOSMOS even when using as few as 1-direction data. This is made possible by a\nnonlinear forward-model that uses the magnitude as an effective prior, for\nwhich we derived a simple gradient descent update rule. We synergistically\ncombine this physics-model with a Variational Network (VN) to leverage the\npower of deep learning in the VaNDI algorithm. This technique adopts the simple\ngradient descent rule from NDI and learns the network parameters during\ntraining, hence requires no additional parameter tuning. Further, we evaluate\nNDI at 7T using highly accelerated Wave-CAIPI acquisitions at 0.5 mm isotropic\nresolution and demonstrate high-quality QSM from as few as 2-direction data.\n