Learning a variational network for reconstruction of accelerated MRI data

Kerstin Hammernik, Teresa Klatzer, Erich Kobler, Michael P. Recht, Daniel K. Sodickson, Thomas Pock, Florian Knoll

Research output: Contribution to journalArticlepeer-review


Purpose: To allow fast and high-quality reconstruction of clinical accelerated multi-coil MR data by learning a variational network that combines the mathematical structure of variational models with deep learning. Theory and Methods: Generalized compressed sensing reconstruction formulated as a variational model is embedded in an unrolled gradient descent scheme. All parameters of this formulation, including the prior model defined by filter kernels and activation functions as well as the data term weights, are learned during an offline training procedure. The learned model can then be applied online to previously unseen data. Results: The variational network approach is evaluated on a clinical knee imaging protocol for different acceleration factors and sampling patterns using retrospectively and prospectively undersampled data. The variational network reconstructions outperform standard reconstruction algorithms, verified by quantitative error measures and a clinical reader study for regular sampling and acceleration factor 4. Conclusion: Variational network reconstructions preserve the natural appearance of MR images as well as pathologies that were not included in the training data set. Due to its high computational performance, that is, reconstruction time of 193 ms on a single graphics card, and the omission of parameter tuning once the network is trained, this new approach to image reconstruction can easily be integrated into clinical workflow. Magn Reson Med 79:3055–3071, 2018.

Original languageEnglish (US)
Pages (from-to)3055-3071
Number of pages17
JournalMagnetic resonance in medicine
Issue number6
StatePublished - Jun 2018


  • accelerated MRI
  • compressed sensing
  • deep learning
  • image reconstruction
  • parallel imaging
  • variational network

ASJC Scopus subject areas

  • Radiology Nuclear Medicine and imaging


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