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