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

Abstract

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.

Deep grey matter quantitative susceptibility mapping from small spatial coverages using deep learning

“…Similar to the conventional U-net [43], the xQSM network [41] comprises two operations, i.e. encoding and decoding, referred to as down-sampling and up-sampling paths.…”

“…Another method, namely QSMnet, [39] proposed by Yoon et al, trained the neural network with in vivo dataset generated from multiple head orientations (i.e., COSMOS) [40]. Recently, Yang et al [41] developed a new deep learning method, named xQSM, by introducing Octave convolution [42] into the U-net [43] architecture to improve the traditional convolutional layers. This Octave convolution network replaced the original convolution into four crossing operations, resulting in high and low-frequency groups of different matrix sizes, which saves storage and reduces the computation redundancy of traditional neural networks.…”

Accelerating quantitative susceptibility and R2* mapping using incoherent undersampling and deep neural network reconstruction

“…phase unwrapping with a best path method [47], magnitude-weighted fitting of multi-echo phase with echo times, background field removal with RESHARP [48], and finally dipole inversion (single-orientation: xQSM [49], multiple orientations: Calculation Of Susceptibility through Multiple Orientation Sampling (COSMOS) [50]).…”

Learn Less, Infer More: Learning in the Fourier Domain for Quantitative Susceptibility Mapping

“…Lai et al ( 2020 ) presented a learned proximal convolutional neural network (LP-CNN) to perform dipole inversion in an iterative proximal gradient descent fashion. Gao et al ( 2020 ) proposed an improved U-Net framework, namely xQSM, for dipole inversion by incorporating octave convolution (OctConv) (Chen et al, 2019 ) layers. Feng et al ( 2021 ) proposed an STI-based deep learning architecture for single-orientation QSM, referred to as MoDL-QSM, which can preserve the nature of anisotropic magnetic susceptibility in brain white matter (WM).…”