# Affine Transformation Edited and Refined Deep Neural Network for Quantitative Susceptibility Mapping

arXiv: https://arxiv.org/abs/2211.13942 · HTML: https://mlsanity.com/paper/2211.13942/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Efficient and Accurate MRI Super-Resolution using a Generative Adversarial Network and 3D Multi-Level Densely Connected Network](https://mlsanity.com/paper/1803.01417/) (2018)
- [Brain MRI Super Resolution Using 3D Deep Densely Connected Neural Networks](https://mlsanity.com/paper/1801.02728/) (2018)
- [Quantitative Susceptibility Mapping using Deep Neural Network: QSMnet](https://mlsanity.com/paper/1803.05627/) (2018)
- [Fidelity Imposed Network Edit (FINE) for Solving Ill-Posed Image Reconstruction](https://mlsanity.com/paper/1905.07284/) (2019)
- [Exploring linearity of deep neural network trained QSM: QSMnet+](https://mlsanity.com/paper/1909.07716/) (2019)
- [QSMGAN: Improved Quantitative Susceptibility Mapping using 3D Generative Adversarial Networks with Increased Receptive Field](https://mlsanity.com/paper/1905.03356/) (2019)
- [Learned Proximal Networks for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2008.05024/) (2020)
- [MoDL-QSM: Model-based Deep Learning for Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2101.08413/) (2021)
- [Learning-based Single-step Quantitative Susceptibility Mapping Reconstruction Without Brain Extraction](https://mlsanity.com/paper/1905.05953/) (2019)
- [Instant tissue field and magnetic susceptibility mapping from MR raw phase using Laplacian enabled deep neural networks](https://mlsanity.com/paper/2111.07665/) (2021)

## Built on by (most cited first, 2 of 2)

- [Quantitative Susceptibility Mapping through Model-based Deep Image Prior (MoDIP)](https://mlsanity.com/paper/2308.09467/) (2023)
- [IR2QSM: Quantitative Susceptibility Mapping via Deep Neural Networks with Iterative Reverse Concatenations and Recurrent Modules](https://mlsanity.com/paper/2406.12300/) (2024)

## Abstract (arXiv)

Deep neural networks have demonstrated great potential in solving dipole inversion for Quantitative Susceptibility Mapping (QSM). However, the performances of most existing deep learning methods drastically degrade with mismatched sequence parameters such as acquisition orientation and spatial resolution. We propose an end-to-end AFfine Transformation Edited and Refined (AFTER) deep neural network for QSM, which is robust against arbitrary acquisition orientation and spatial resolution up to 0.6 mm isotropic at the finest. The AFTER-QSM neural network starts with a forward affine transformation layer, followed by an Unet for dipole inversion, then an inverse affine transformation layer, followed by a Residual Dense Network (RDN) for QSM refinement. Simulation and in-vivo experiments demonstrated that the proposed AFTER-QSM network architecture had excellent generalizability. It can successfully reconstruct susceptibility maps from highly oblique and anisotropic scans, leading to the best image quality assessments in simulation tests and suppressed streaking artifacts and noise levels for in-vivo experiments compared with other methods. Furthermore, ablation studies showed that the RDN refinement network significantly reduced image blurring and susceptibility underestimation due to affine transformations. In addition, the AFTER-QSM network substantially shortened the reconstruction time from minutes using conventional methods to only a few seconds.