  Quantitative susceptibility mapping (QSM) is a useful magnetic resonance
imaging (MRI) technique which provides spatial distribution of magnetic
susceptibility values of tissues. QSMs can be obtained by deconvolving the
dipole kernel from phase images, but the spectral nulls in the dipole kernel
make the inversion ill-posed. In recent times, deep learning approaches have
shown a comparable QSM reconstruction performance as the classic approaches,
despite the fast reconstruction time. Most of the existing deep learning
methods are, however, based on supervised learning, so matched pairs of input
phase images and the ground-truth maps are needed. Moreover, it was reported
that the supervised learning often leads to underestimated QSM values. To
address this, here we propose a novel unsupervised QSM deep learning method
using physics-informed cycleGAN, which is derived from optimal transport
perspective. In contrast to the conventional cycleGAN, our novel cycleGAN has
only one generator and one discriminator thanks to the known dipole kernel.
Experimental results confirm that the proposed method provides more accurate
QSM maps compared to the existing deep learning approaches, and provide
competitive performance to the best classical approaches despite the ultra-fast
reconstruction.
