Unsupervised deep learning with convolutional neural networks for static parallel transmit design: A retrospective study

Toygan Kilic, Patrick Liebig, Omer Burak Demirel, Jürgen Herrler, Armin M. Nagel, Kamil Ugurbil, Mehmet Akçakaya

Research output: Contribution to journalArticlepeer-review


Purpose: To mitigate (Formula presented.) inhomogeneity at 7T for multi-channel transmit arrays using unsupervised deep learning with convolutional neural networks (CNNs). Methods: Deep learning parallel transmit (pTx) pulse design has received attention, but such methods have relied on supervised training and did not use CNNs for multi-channel (Formula presented.) maps. In this work, we introduce an alternative approach that facilitates the use of CNNs with multi-channel (Formula presented.) maps while performing unsupervised training. The multi-channel (Formula presented.) maps are concatenated along the spatial dimension to enable shift-equivariant processing amenable to CNNs. Training is performed in an unsupervised manner using a physics-driven loss function that minimizes the discrepancy of the Bloch simulation with the target magnetization, which eliminates the calculation of reference transmit RF weights. The training database comprises 3824 2D sagittal, multi-channel (Formula presented.) maps of the healthy human brain from 143 subjects. (Formula presented.) data were acquired at 7T using an 8Tx/32Rx head coil. The proposed method is compared to the unregularized magnitude least-squares (MLS) solution for the target magnetization in static pTx design. Results: The proposed method outperformed the unregularized MLS solution for RMS error and coefficient-of-variation and had comparable energy consumption. Additionally, the proposed method did not show local phase singularities leading to distinct holes in the resulting magnetization unlike the unregularized MLS solution. Conclusion: Proposed unsupervised deep learning with CNNs performs better than unregularized MLS in static pTx for speed and robustness.

Original languageEnglish (US)
Pages (from-to)2498-2507
Number of pages10
JournalMagnetic resonance in medicine
Issue number6
StateAccepted/In press - 2024

Bibliographical note

Publisher Copyright:
© 2024 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals LLC on behalf of International Society for Magnetic Resonance in Medicine.


  • 7 T
  • RF inhomogeneity mitigation
  • convolutional neural networks
  • deep learning
  • parallel excitation
  • unsupervised learning


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