Probabilistic dipole inversion for adaptive quantitative susceptibility mapping

Jinwei Zhang1,2, Hang Zhang1,2, Mert Sabuncu1,2, Pascal Spincemaille2, Thanh Nguyen2, Yi Wang3,2
1: Cornell University, Ithaca, 2: Weill Medical College of Cornell University, New York, 3: Cornell University, Ithac
MIDL 2020 special issue
Publication date: 2021/03/12
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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. Our code is available at


quantitative susceptibility mapping · convolutional neural network · uncertainty estimation · variational inference

Bibtex @article{melba:2021:003:zhang, title = "Probabilistic dipole inversion for adaptive quantitative susceptibility mapping", author = "Zhang, Jinwei and Zhang, Hang and Sabuncu, Mert and Spincemaille, Pascal and Nguyen, Thanh and Wang, Yi", journal = "Machine Learning for Biomedical Imaging", volume = "1", issue = "MIDL 2020 special issue", year = "2021", issn = "2766-905X", url = "" }
RISTY - JOUR AU - Zhang, Jinwei AU - Zhang, Hang AU - Sabuncu, Mert AU - Spincemaille, Pascal AU - Nguyen, Thanh AU - Wang, Yi PY - 2021 TI - Probabilistic dipole inversion for adaptive quantitative susceptibility mapping T2 - Machine Learning for Biomedical Imaging VL - 1 IS - MIDL 2020 special issue SN - 2766-905X UR - ER -

2021:003 cover