Bayesian Learning of Probabilistic Dipole Inversion for Quantitative Susceptibility Mapping

Jinwei Zhang, Hang Zhang, Mert Sabuncu, Pascal Spincemaille, Thanh Nguyen, Yi Wang
Proceedings of the Third Conference on Medical Imaging with Deep Learning, PMLR 121:892-902, 2020.

Abstract

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’ data 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 CNN’s weights in an unsupervised fashion by minimizing the {\em Kullback-Leibler} divergence between the approximated posterior distribution represented by CNN and the true posterior distribution given the likelihood distribution from known physical model and pre-defined 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v121-zhang20b, title = {Bayesian Learning of Probabilistic Dipole Inversion for Quantitative Susceptibility Mapping}, author = {Zhang, Jinwei and Zhang, Hang and Sabuncu, Mert and Spincemaille, Pascal and Nguyen, Thanh and Wang, Yi}, booktitle = {Proceedings of the Third Conference on Medical Imaging with Deep Learning}, pages = {892--902}, year = {2020}, editor = {Arbel, Tal and Ben Ayed, Ismail and de Bruijne, Marleen and Descoteaux, Maxime and Lombaert, Herve and Pal, Christopher}, volume = {121}, series = {Proceedings of Machine Learning Research}, month = {06--08 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v121/zhang20b/zhang20b.pdf}, url = {https://proceedings.mlr.press/v121/zhang20b.html}, abstract = {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’ data 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 CNN’s weights in an unsupervised fashion by minimizing the {\em Kullback-Leibler} divergence between the approximated posterior distribution represented by CNN and the true posterior distribution given the likelihood distribution from known physical model and pre-defined 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.} }
Endnote
%0 Conference Paper %T Bayesian Learning of Probabilistic Dipole Inversion for Quantitative Susceptibility Mapping %A Jinwei Zhang %A Hang Zhang %A Mert Sabuncu %A Pascal Spincemaille %A Thanh Nguyen %A Yi Wang %B Proceedings of the Third Conference on Medical Imaging with Deep Learning %C Proceedings of Machine Learning Research %D 2020 %E Tal Arbel %E Ismail Ben Ayed %E Marleen de Bruijne %E Maxime Descoteaux %E Herve Lombaert %E Christopher Pal %F pmlr-v121-zhang20b %I PMLR %P 892--902 %U https://proceedings.mlr.press/v121/zhang20b.html %V 121 %X 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’ data 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 CNN’s weights in an unsupervised fashion by minimizing the {\em Kullback-Leibler} divergence between the approximated posterior distribution represented by CNN and the true posterior distribution given the likelihood distribution from known physical model and pre-defined 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.
APA
Zhang, J., Zhang, H., Sabuncu, M., Spincemaille, P., Nguyen, T. & Wang, Y.. (2020). Bayesian Learning of Probabilistic Dipole Inversion for Quantitative Susceptibility Mapping. Proceedings of the Third Conference on Medical Imaging with Deep Learning, in Proceedings of Machine Learning Research 121:892-902 Available from https://proceedings.mlr.press/v121/zhang20b.html.

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