# Exploring linearity of deep neural network trained QSM: QSMnet+

arXiv: https://arxiv.org/abs/1909.07716 · HTML: https://mlsanity.com/paper/1909.07716/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2019.

## Built on by (most cited first, 11 of 11)

- [Physics-driven Synthetic Data Learning for Biomedical Magnetic Resonance](https://mlsanity.com/paper/2203.11178/) (2022)
- [One for Multiple: Physics-informed Synthetic Data Boosts Generalizable Deep Learning for Fast MRI Reconstruction](https://mlsanity.com/paper/2307.13220/) (2023)
- [MoDL-QSM: Model-based Deep Learning for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2101.08413/) (2021)
- [Quantitative Susceptibility Mapping through Model-based Deep Image Prior (MoDIP)](https://mlsanity.com/paper/2308.09467/) (2023)
- [Improved Padding in CNNs for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2106.15331/) (2021)
- [Affine Transformation Edited and Refined Deep Neural Network for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2211.13942/) (2022)
- [DeepSTI: Towards Tensor Reconstruction using Fewer Orientations in Susceptibility Tensor Imaging](https://mlsanity.com/paper/2209.04504/) (2022)
- [LapGM: A Multisequence MR Bias Correction and Normalization Model](https://mlsanity.com/paper/2209.13619/) (2022)
- [Amide Proton Transfer (APT) imaging in tumor with a machine learning approach using partially synthetic data](https://mlsanity.com/paper/2311.01683/) (2023)
- [IR2QSM: Quantitative Susceptibility Mapping via Deep Neural Networks with Iterative Reverse Concatenations and Recurrent Modules](https://mlsanity.com/paper/2406.12300/) (2024)
- [HARP: HARmonizing in-vivo diffusion MRI using Phantom-only training](https://mlsanity.com/paper/2603.06696/) (2026)

## Abstract (arXiv)

Recently, deep neural network-powered quantitative susceptibility mapping (QSM), QSMnet, successfully performed ill conditioned dipole inversion in QSM and generated high-quality susceptibility maps. In this paper, the network, which was trained by healthy volunteer data, is evaluated for hemorrhagic lesions that have substantially higher susceptibility than healthy tissues in order to test linearity of QSMnet for susceptibility. The results show that QSMnet underestimates susceptibility in hemorrhagic lesions, revealing degraded linearity of the network for the untrained susceptibility range. To overcome this limitation, a data augmentation method is proposed to generalize the network for a wider range of susceptibility. The newly trained network, which is referred to as QSMnet+, is assessed in computer-simulated lesions with an extended susceptibility range (-1.4 ppm to +1.4 ppm) and also in twelve hemorrhagic patients. The simulation results demonstrate improved linearity of QSMnet+ over QSMnet (root mean square error of QSMnet+: 0.04 ppm vs. QSMnet: 0.36 ppm). When applied to patient data, QSMnet+ maps show less noticeable artifacts to those of conventional QSM maps. Moreover, the susceptibility values of QSMnet+ in hemorrhagic lesions are better matched to those of the conventional QSM method than those of QSMnet when analyzed using linear regression (QSMnet+: slope = 1.05, intercept = -0.03, R2 = 0.93; QSMnet: slope = 0.68, intercept = 0.06, R2 = 0.86), consolidating improved linearity in QSMnet+. This study demonstrates the importance of the trained data range in deep neural network-powered parametric mapping and suggests the data augmentation approach for generalization of network. The new network can be applicable for a wide range of susceptibility quantification.