# Bayesian Learning of Probabilistic Dipole Inversion for Quantitative Susceptibility Mapping

arXiv: https://arxiv.org/abs/2004.12573 · HTML: https://mlsanity.com/paper/2004.12573/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2020.

## Built on by (most cited first, 4 of 4)

- [LARO: Learned Acquisition and Reconstruction Optimization to accelerate Quantitative Susceptibility Mapping](https://mlsanity.com/paper/2211.00725/) (2022)
- [NeRD: Neural Representation of Distribution for Medical Image Segmentation](https://mlsanity.com/paper/2103.04020/) (2021)
- [Uncertainty-Aware Self-supervised Neural Network for Liver T1ρ Mapping with Relaxation Constraint](https://mlsanity.com/paper/2207.03105/) (2022)
- [High-pass filtered fidelity-imposed network edit (HP-FINE) for robust quantitative susceptibility mapping from high-pass filtered phase](https://mlsanity.com/paper/2305.03844/) (2023)

## Abstract (arXiv)

A learning-based posterior distribution estimation method, Probabilistic Dipole Inversion (PDI), is proposed to solve quantitative susceptibility mapping (QSM) inverse problem in MRI with uncertainty estimation. A deep convolutional neural network (CNN) is used to represent the multivariate Gaussian distribution as the approximated posterior distribution of susceptibility given the input measured field. In PDI, such CNN is firstly trained on healthy subjects dataset with labels by maximizing the posterior Gaussian distribution loss function as used in Bayesian deep learning. When tested on new dataset without any label, PDI updates the pre-trained network in an unsupervised fashion by minimizing the KL divergence between the approximated posterior distribution represented by CNN and the true posterior distribution given the likelihood distribution from known physical model and prior distribution. Based on our experiments, PDI provides additional uncertainty estimation compared to the conventional MAP approach, meanwhile addressing the potential discrepancy issue of CNN when test data deviates from training dataset.