xQSM: quantitative susceptibility mapping with octave convolutional and noise-regularized neural networks

Quantitative susceptibility mapping (QSM) provides a valuable MRI contrast mechanism that has demonstrated broad clinical applications. However, the image reconstruction of QSM is challenging due to its ill-posed dipole inversion process. In this study, a new deep learning method for QSM reconstruction, namely xQSM, was designed by introducing noise regularization and modified octave convolutional layers into a U-net backbone and trained with synthetic and in vivo datasets, respectively. The xQSM method was compared with two recent deep learning (QSMnet⁺ and DeepQSM) and two conventional dipole inversion (MEDI and iLSQR) methods, using both digital simulations and in vivo experiments. Reconstruction error metrics, including peak signal-to-noise ratio, structural similarity, normalized root mean squared error and deep gray matter susceptibility measurements, were evaluated for comparison of the different methods. The results showed that the proposed xQSM network trained with in vivo datasets achieved the best reconstructions of all the deep learning methods. In particular, it led to, on average, 32.3%, 25.4% and 11.7% improvement in the accuracy of globus pallidus susceptibility estimation for digital simulations and 39.3%, 21.8% and 6.3% improvements for in vivo acquisitions compared with DeepQSM, QSMnet⁺ and iLSQR, respectively. It also exhibited the highest linearity against different susceptibility intensity scales and demonstrated the most robust generalization capability to various spatial resolutions of all the deep learning methods. In addition, the xQSM method also substantially shortened the reconstruction time from minutes using MEDI to only a few seconds.