Quantitative susceptibility mapping (QSM) reveals pathological changes in widespread diseases such as Parkinson's disease, Multiple Sclerosis, or hepatic iron overload. QSM requires multiple processing steps after the acquisition of magnetic resonance imaging (MRI) phase measurements such as unwrapping, background field removal and the solution of an ill-posed field-to-source-inversion. Current techniques utilize iterative optimization procedures to solve the inversion and background field correction, which are computationally expensive and lead to suboptimal or over-regularized solutions requiring a careful choice of parameters that make a clinical application of QSM challenging. We have previously demonstrated that a deep convolutional neural network can invert the magnetic dipole kernel with a very efficient feed forward multiplication not requiring iterative optimization or the choice of regularization parameters. In this work, we extended this approach to remove background fields in QSM. The prototype method, called SHARQnet, was trained on simulated background fields and tested on 3 T and 7 T brain datasets. We show that SHARQnet outperforms current background field removal procedures and generalizes to a wide range of input data without requiring any parameter adjustments. In summary, we demonstrate that the solution of ill-posed problems in QSM can be achieved by learning the underlying physics causing the artifacts and removing them in an efficient and reliable manner and thereby will help to bring QSM towards clinical applications.

Quantitative susceptibility mapping (QSM) reveals pathological changes in widespread diseases such as Parkinson's disease, Multiple Sclerosis, or hepatic iron overload. QSM requires multiple processing steps after the acquisition of magnetic resonance imaging (MRI) phase measurements such as unwrapping, background field removal and the solution of an ill-posed field-to-source-inversion. Current techniques utilize iterative optimization procedures to solve the inversion and background field correction, which are computationally expensive and lead to suboptimal or over-regularized solutions requiring a careful choice of parameters that make a clinical application of QSM challenging. We have previously demonstrated that a deep convolutional neural network can invert the magnetic dipole kernel with a very efficient feed forward multiplication not requiring iterative optimization or the choice of regularization parameters. In this work, we extended this approach to remove background fields in QSM. The prototype method, called SHARQnet, was trained on simulated background fields and tested on 3T and 7T brain datasets. We show that SHARQnet outperforms current background field removal procedures and generalizes to a wide range of input data without requiring any parameter adjustments. In summary, we demonstrate that the solution of ill-posed problems in QSM can be achieved by learning the underlying physics causing the artifacts and removing them in an efficient and reliable manner and thereby will help to bring QSM towards clinical applications.