Skip to main content

Neural Implicit k-space with Trainable Periodic Activation Functions for Cardiac MR Imaging

  • Conference paper
  • First Online:
Bildverarbeitung für die Medizin 2024 (BVM 2024)

Abstract

In MRI reconstruction, neural implicit k-space (NIK) representation maps spatial frequencies to k-space intensity values using an MLP with periodic activation functions. However, the choice of hyperparameters for periodic activation functions is challenging and influences training stability. In this work, we introduce and study the effectiveness of trainable (non-)periodic activation functions for NIK in the context of non-Cartesian Cardiac MRI. Evaluated on 42 radially sampled datasets from 6 subjects, NIKs with the proposed trainable activation functions outperform qualitatively and quantitatively other state-of-the-art reconstruction methods, including NIK with fixed periodic activation functions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Chen Z, Zhang H. Learning implicit fields for generative shape modeling. Proc IEEE CVPR. 2019:5939–48.

    Google Scholar 

  2. Huang W, Li HB, Pan J, Cruz G, Rueckert D, Hammernik K. Neural implicit k-space for binning-free non-aartesian cardiac MR imaging. Proc MICCAI. Springer. 2023:548–60.

    Google Scholar 

  3. Wolterink JM, Zwienenberg JC, Brune C. Implicit neural representations for deformable image registration. Int Conf Med Imag Deep Learn. 2022:1349–59.

    Google Scholar 

  4. Zimmer V, Hammernik K, et al. Towards generalised neural implicit representations for image registration. DGM4MICCAI@MICCAI. 2023, in print.

    Google Scholar 

  5. Mildenhall B, Srinivasan PP, Tancik M, Barron JT, Ramamoorthi R, Ng R. NeRF: representing scenes as neural radiance fields for view synthesis. Commun ACM. 2021;65(1):99– 106.

    Google Scholar 

  6. Sitzmann V, Martel J, Bergman A, Lindell D, Wetzstein G. Implicit neural representations with periodic activation functions. Adv Neural Inf Process Syst. 2020;33:7462–73.

    Google Scholar 

  7. Saragadam V, LeJeune D, Tan J, Balakrishnan G, Veeraraghavan A, Baraniuk RG. WIRE: wavelet implicit neural representations. Proc IEEE CVPR. 2023:18507–16.

    Google Scholar 

  8. Agostinelli F, Hoffman M, Sadowski P, Baldi P. Learning activation functions to improve deep neural networks. arXiv preprint arXiv:1412.6830. 2014.

  9. Chen Y, Pock T. Trainable nonlinear reaction diffusion: a flexible framework for fast and effective image restoration. IEEE Trans Pattern Anal Mach Intell. 2016;39(6):1256–72.

    Google Scholar 

  10. Kobler E, Klatzer T, Hammernik K, Pock T. Variational networks: connecting variational methods and deep learning. Proc GCPR. Springer. 2017:281–93.

    Google Scholar 

  11. Hammernik K, Klatzer T, Kobler E, Recht MP, Sodickson DK, Pock T et al. Learning a variational network for reconstruction of accelerated MRI data. Magn Reson Med. 2018;79(6):3055–71.

    Google Scholar 

  12. Tancik M, Srinivasan P, Mildenhall B, Fridovich-Keil S, Raghavan N, SinghalUet al. Fourier features let networks learn high frequency functions in low dimensional domains. Adv Neural Inf Process Syst. 2020;33:7537–47.

    Google Scholar 

  13. Mildenhall B, Hedman P, Martin-Brualla R, Srinivasan PP, Barron JT. NeRF in the dark: high dynamic range viewsynthesis from noisy rawimages. Proc IEEE CVPR. 2022:16190–9.

    Google Scholar 

  14. Pruessmann KP, Weiger M, Börnert P, Boesiger P. Advances in sensitivity encoding with arbitrary k-Space trajectories. Magn Reson Med. 2001;46(4):638–51.

    Google Scholar 

  15. Otazo R, Candes E, Sodickson DK. Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components. Magn Reson Med. 2015;73(3):1125–36.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Patrick T. Haft .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2024 Der/die Autor(en), exklusiv lizenziert an Springer Fachmedien Wiesbaden GmbH, ein Teil von Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Haft, P.T., Huang, W., Cruz, G., Rueckert, D., Zimmer, V.A., Hammernik, K. (2024). Neural Implicit k-space with Trainable Periodic Activation Functions for Cardiac MR Imaging. In: Maier, A., Deserno, T.M., Handels, H., Maier-Hein, K., Palm, C., Tolxdorff, T. (eds) Bildverarbeitung für die Medizin 2024. BVM 2024. Informatik aktuell. Springer Vieweg, Wiesbaden. https://doi.org/10.1007/978-3-658-44037-4_26

Download citation

Publish with us

Policies and ethics