Probabilistic Dipole Inversion for Adaptive Quantitative Susceptibility Mapping

TL;DR

This paper introduces Probabilistic Dipole Inversion (PDI), a deep learning method for quantitative susceptibility mapping in MRI that estimates uncertainty and adapts to new pathologies without supervised retraining.

Contribution

The paper presents a novel deep learning-based Bayesian approach for QSM that estimates posterior distributions and adapts to new data domains in an unsupervised manner.

Findings

PDI provides uncertainty estimates surpassing traditional MAP methods.

PDI effectively adapts to new pathologies without supervised retraining.

Experimental results demonstrate improved robustness and uncertainty quantification.

Abstract

A learning-based posterior distribution estimation method, Probabilistic Dipole Inversion (PDI), is proposed to solve the quantitative susceptibility mapping (QSM) inverse problem in MRI with uncertainty estimation. In PDI, a deep convolutional neural network (CNN) is used to represent the multivariate Gaussian distribution as the approximate posterior distribution of susceptibility given the input measured field. Such CNN is first trained on healthy subjects via posterior density estimation, where the training dataset contains samples from the true posterior distribution. Domain adaptations are then deployed on patient datasets with new pathologies not included in pre-training, where PDI updates the pre-trained CNN's weights in an unsupervised fashion by minimizing the Kullback-Leibler divergence between the approximate posterior distribution represented by CNN and the true posterior distribution from the likelihood distribution of a known physical model and pre-defined prior distribution. Based on our experiments, PDI provides additional uncertainty estimation compared to the conventional MAP approach, while addressing the potential issue of the pre-trained CNN when test data deviates from training.