Skip to main content

HyperRecon: Regularization-Agnostic CS-MRI Reconstruction with Hypernetworks

  • Conference paper
  • First Online:
Machine Learning for Medical Image Reconstruction (MLMIR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12964))

Abstract

Reconstructing under-sampled k-space measurements in Compressed Sensing MRI (CS-MRI) is classically solved by minimizing a regularized least-squares cost function. In the absence of fully-sampled training data, this optimization approach can still be amortized via a neural network that minimizes the cost function over a dataset of under-sampled measurements. Here, a crucial design choice is the regularization function(s) and corresponding weight(s). In this paper, we introduce HyperRecon – a novel strategy of using a hypernetwork to generate the parameters of a main reconstruction network as a function of the regularization weight(s), resulting in a regularization-agnostic reconstruction model. At test time, for a given under-sampled image, our model can rapidly compute reconstructions with different amounts of regularization. We propose and empirically demonstrate an efficient and data-driven way of maximizing reconstruction performance given limited hypernetwork capacity. Our code will be made publicly available upon acceptance.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In this paper, we assume a single coil acquisition.

  2. 2.

    For baselines, the \(18 \times 18\) grid was linearly interpolated to \(100 \times 100\) to match the hypernetwork landscapes.

References

  1. Aggarwal, H.K., Mani, M.P., Jacob, M.: MoDL: Model-based deep learning architecture for inverse problems. IEEE Trans. Med. 38(2), 394–405 (2019)

    Article  Google Scholar 

  2. Balakrishnan, G., Zhao, A., Sabuncu, M.R., Guttag, J., Dalca, A.V.: Voxelmorph: a learning framework for deformable medical image registration. IEEE Trans. Med. 38(8), 1788–1800 (2019)

    Article  Google Scholar 

  3. Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Img. Sci. 2(1), 183–202 (2009)

    Article  MathSciNet  Google Scholar 

  4. Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)

    Article  Google Scholar 

  5. Brock, A., Lim, T., Ritchie, J., Weston, N.: SMASH: one-shot model architecture search through hypernetworks. In: ICLR (2018)

    Google Scholar 

  6. Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imag. Vis. 40, 120–145 (2011)

    Google Scholar 

  7. Chang, O., Flokas, L., Lipson, H.: Principled weight initialization for hypernetworks. In: ICLR (2020)

    Google Scholar 

  8. Chauffert, N., Ciuciu, P., Weiss, P.: Variable density compressed sensing in MRI. theoretical vs heuristic sampling strategies. In: 2013 IEEE 10th ISBI, April 2013

    Google Scholar 

  9. Combettes, P.L., Pesquet, J.C.: Proximal splitting methods in signal processing (2009)

    Google Scholar 

  10. Cremer, C., Li, X., Duvenaud, D.: Inference suboptimality in variational autoencoders (2018)

    Google Scholar 

  11. Dalca, A.V., Guttag, J., Sabuncu, M.R.: Anatomical priors in convolutional networks for unsupervised biomedical segmentation. In: IEEE CVPR, June 2018

    Google Scholar 

  12. Daubechies, I., Defrise, M., Mol, C.D.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Pure Appl. Math. 57, 1413–1457 (2003)

    Google Scholar 

  13. Figueiredo, M.A.T., Nowak, R.D.: An FM algorithm for wavelet-based image restoration. IEEE Trans. Image Process. 12(8), 906–916 (2003)

    Article  MathSciNet  Google Scholar 

  14. Geethanath, S., et al.: Compressed sensing MRI: a review. Crit. Rev. Biomed. Eng. 41(3), 183–204 (2013)

    Google Scholar 

  15. Gershman, S.J., Goodman, N.D.: Amortized inference in probabilistic reasoning. In: CogSci (2014)

    Google Scholar 

  16. Ha, D., Dai, A., Le, Q.V.: Hypernetworks (2016)

    Google Scholar 

  17. Hoopes, A., Hoffmann, M., Fischl, B., Guttag, J., Dalca, A.V.: Hypermorph: amortized hyperparameter learning for image registration. arXiv preprint arXiv:2101.01035 (2021)

  18. Hu, Y., Jacob, M.: Higher degree total variation (HDTV) regularization for image recovery. IEEE Trans. Image Process. 21(5), 2559–2571 (2012)

    Article  MathSciNet  Google Scholar 

  19. Kingma, D.P., Welling, M.: Auto-encoding variational bayes (2014)

    Google Scholar 

  20. Klocek, S., Maziarka, L., Wolczyk, M., Tabor, J., Nowak, J., Śmieja, M.: Hypernetwork functional image representation. Lecture Notes in Computer Science, pp. 496–510. (2019)

    Google Scholar 

  21. Krueger, D., Huang, C.W., Islam, R., Turner, R., Lacoste, A., Courville, A.: Bayesian hypernetworks (2018)

    Google Scholar 

  22. Lorraine, J., Duvenaud, D.: Stochastic hyperparameter optimization through hypernetworks (2018)

    Google Scholar 

  23. Luo, G.: A review of automatic selection methods for machine learning algorithms and hyper-parameter values. Netw. Model Anal. Health Inform. Bioinforma. 5, 18 (2016). https://doi.org/10.1007/s13721-016-0125-6

  24. Lustig, M., Donoho, D., Pauly, J.M.: Sparse MRI the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58(6), 1182–1195 (2007)

    Article  Google Scholar 

  25. Marino, J., Yue, Y., Mandt, S.: Iterative amortized inference. arXiv preprint arXiv:1807.09356 (2018)

  26. Pan, Z., Liang, Y., Zhang, J., Yi, X., Yu, Y., Zheng, Y.: Hyperst-net: hypernetworks for spatio-temporal forecasting (2018)

    Google Scholar 

  27. Ravishankar, S., Ye, J.C., Fessler, J.A.: Image reconstruction: from sparsity to data-adaptive methods and machine learning. Proc. IEEE 108(1), 86–109 (2020)

    Article  Google Scholar 

  28. Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28

    Chapter  Google Scholar 

  29. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D Nonlin. Phenomena 60(1–4), 259–268 (1992)

    Article  MathSciNet  Google Scholar 

  30. Shahriari, B., Swersky, K., Wang, Z., Adams, R.P., de Freitas, N.: Taking the human out of the loop: a review of Bayesian optimization. Proc. IEEE 104(1), 148–175 (2016)

    Article  Google Scholar 

  31. Shen, F., Yan, S., Zeng, G.: Meta networks for neural style transfer (2017)

    Google Scholar 

  32. Shu, R., Bui, H.H., Zhao, S., Kochenderfer, M.J., Ermon, S.: Amortized inference regularization (2018)

    Google Scholar 

  33. Ukai, K., Matsubara, T., Uehara, K.: Hypernetwork-based implicit posterior estimation and model averaging of CNN. In: Zhu, J., Takeuchi, I. (eds.) Proceedings of The 10th Asian Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 95, pp. 176–191. PMLR, November 2018

    Google Scholar 

  34. Wang, A.Q., Dalca, A.V., Sabuncu, M.R.: Neural network-based reconstruction in compressed sensing MRI without fully-sampled training data. In: Deeba, F., Johnson, P., Würfl, T., Ye, J.C. (eds.) Machine Learning for Medical Image Reconstruction, pp. 27–37. Springer International Publishing, Cham (2020)

    Chapter  Google Scholar 

  35. Wang, S., et al.: Accelerating magnetic resonance imaging via deep learning. In: 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI), pp. 514–517 (2016)

    Google Scholar 

  36. Yang, G., et al.: Dagan: deep de-aliasing generative adversarial networks for fast compressed sensing MRI reconstruction. IEEE Trans. Med. Imag. 37(6), 1310–1321 (2018)

    Google Scholar 

  37. Yang, Y., Sun, J., Li, H., Xu, Z.: Deep admm-net for compressive sensing MRI. In: Lee, D., Sugiyama, M., Luxburg, U., Guyon, I., Garnett, R. (eds.) Advances in Neural Information Processing Systems. vol. 29. Curran Associates, Inc. Barcelona (2016)

    Google Scholar 

  38. Ye, N., Roosta-Khorasani, F., Cui, T.: Optimization methods for inverse problems. In: Wood, D., de Gier, J., Praeger, C., Tao, T. (eds.) 2017 MATRIX Annals. MATRIX Book Series, vol. 2, pp. 121–140. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04161-8_9

  39. Yin, W., Osher, S., Goldfarb, D., Darbon, J.: Bregman iterative algorithms for \(l_1\)-minimization with applications to compressed sensing. SIAM J. Imag. Sci. 1(1), 143–168 (2008)

    Google Scholar 

  40. Yu, T., Zhu, H.: Hyperparameter optimization. In: Hutter, F., Kotthoff, L., Vanschoren, J. (eds.) Automated Machine Learning. The Springer Series on Challenges in Machine Learning. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-05318-5_1

  41. Zhang, C., Ren, M., Urtasun, R.: Graph hypernetworks for neural architecture search (2019)

    Google Scholar 

Download references

Acknowledgements

This work was supported by NIH grants R01LM012719 (MS), R01AG053949 (MS), 1R01AG064027 (AD), the NSF NeuroNex grant 1707312 (MS), and the NSF CAREER 1748377 grant (MS).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alan Q. Wang .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Wang, A.Q., Dalca, A.V., Sabuncu, M.R. (2021). HyperRecon: Regularization-Agnostic CS-MRI Reconstruction with Hypernetworks. In: Haq, N., Johnson, P., Maier, A., Würfl, T., Yoo, J. (eds) Machine Learning for Medical Image Reconstruction. MLMIR 2021. Lecture Notes in Computer Science(), vol 12964. Springer, Cham. https://doi.org/10.1007/978-3-030-88552-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-88552-6_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-88551-9

  • Online ISBN: 978-3-030-88552-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics