Learned Proximal Networks for Quantitative Susceptibility Mapping

Kuo Wei Lai, Manisha Aggarwal, Peter van Zijl, Xu Li, Jeremias Sulam

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Quantitative Susceptibility Mapping (QSM) estimates tissue magnetic susceptibility distributions from Magnetic Resonance (MR) phase measurements by solving an ill-posed dipole inversion problem. Conventional single orientation QSM methods usually employ regularization strategies to stabilize such inversion, but may suffer from streaking artifacts or over-smoothing. Multiple orientation QSM such as calculation of susceptibility through multiple orientation sampling (COSMOS) can give well-conditioned inversion and an artifact free solution but has expensive acquisition costs. On the other hand, Convolutional Neural Networks (CNN) show great potential for medical image reconstruction, albeit often with limited interpretability. Here, we present a Learned Proximal Convolutional Neural Network (LP-CNN) for solving the ill-posed QSM dipole inversion problem in an iterative proximal gradient descent fashion. This approach combines the strengths of data-driven restoration priors and the clear interpretability of iterative solvers that can take into account the physical model of dipole convolution. During training, our LP-CNN learns an implicit regularizer via its proximal, enabling the decoupling between the forward operator and the data-driven parameters in the reconstruction algorithm. More importantly, this framework is believed to be the first deep learning QSM approach that can naturally handle an arbitrary number of phase input measurements without the need for any ad-hoc rotation or re-training. We demonstrate that the LP-CNN provides state-of-the-art reconstruction results compared to both traditional and deep learning methods while allowing for more flexibility in the reconstruction process.

Original languageEnglish (US)
Title of host publicationMedical Image Computing and Computer Assisted Intervention – MICCAI 2020 - 23rd International Conference, Proceedings
EditorsAnne L. Martel, Purang Abolmaesumi, Danail Stoyanov, Diana Mateus, Maria A. Zuluaga, S. Kevin Zhou, Daniel Racoceanu, Leo Joskowicz
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages11
ISBN (Print)9783030597122
StatePublished - 2020
Event23rd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2020 - Lima, Peru
Duration: Oct 4 2020Oct 8 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12262 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2020


  • Deep learning
  • Proximal learning
  • Quantitative Susceptibility Mapping

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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