Abstract
In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised learning protocols that are competitive with supervised approaches in performance. Motivated by the maximum-likelihood principle, we propose an unsupervised learning framework for solving ill-posed inverse problems. Instead of seeking pixel-wise proximity between the reconstructed and the ground-truth images, the proposed approach learns an iterative reconstruction network whose output matches the ground-truth in distribution. Considering tomographic reconstruction as an application, we demonstrate that the proposed unsupervised approach not only performs on par with its supervised variant in terms of objective quality measures, but also successfully circumvents the issue of over-smoothing that supervised approaches tend to suffer from. The improvement in reconstruction quality comes at the expense of higher training complexity, but, once trained, the reconstruction time remains the same as its supervised counterpart.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adler, J., Kohr, H., Öktem, O.: Operator discretization library (ODL) (2017). Software https://github.com/odlgroup/odl
Adler, J., Öktem, O.: Solving ill-posed inverse problems using iterative deep neural networks. Inverse Probl. 33(12), 1–24 (2017)
Adler, J., Öktem, O.: Learned primal-dual reconstruction. IEEE Trans. Med. Imaging 37(6), 1322–1332 (2018)
Arjovsky, M., Chintala, S., Bottou, L.: Wasserstein GAN. arXiv:1701.07875v3, December 2017
Arridge, S., Maass, P., Öktem, O., Schönlieb, C.B.: Solving inverse problems using data-driven models. Acta Numerica 28, 1–174 (2019)
Byeongsu, S., Gyutaek, O., Jeongsol, K., Chanyong, J., Ye, J.C.: Optimal transport driven CycleGAN for unsupervised learning in inverse problems. arXiv:1909.12116v4, August 2020
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120–145 (2010)
Gregor, K., LeCun, Y.: Learning fast approximations of sparse coding. In: International Conference on Machine Learning (2010)
Gulrajani1, I., Ahmed, F., Arjovsky, M., Dumoulin, V., Courville, A.: Improved training of Wasserstein GANs. arXiv:1704.00028v3, December 2017
Jin, K.H., McCann, M.T., Froustey, E., Unser, M.: Deep convolutional neural network for inverse problems in imaging. IEEE Trans. Image Process. 26(9), 4509–4522 (2017)
Kobler, E., Effland, A., Kunisch, K., Pock, T.: Total deep variation for linear inverse problems. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 7549–7558 (2020)
Li, H., Schwab, J., Antholzer, S., Haltmeier, M.: NETT: solving inverse problems with deep neural networks. arXiv:1803.00092v3, December 2019
Lin, J., Xia, Y., Qin, T., Chen, Z., Liu, T.: Conditional image-to-image translation. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 5524–5532 (2018)
Lunz, S., Öktem, O., Schönlieb, C.B.: Adversarial regularizers in inverse problems. In: Advances in Neural Information Processing Systems, pp. 8507–8516 (2018)
McCollough, C.: TFG-207a-04: overview of the low dose CT grand challenge. Med. Phys. 43(6), 3759–3760 (2014)
Meinhardt, T., Moller, M., Hazirbas, C., Cremers, D.: Learning proximal operators: using denoising networks for regularizing inverse imaging problems. In: Proceedings of the IEEE International Conference on Computer Vision pp. 1781–1790 (2017)
Scherzer, O., Grasmair, M., Grossauer, H., Haltmeier, M., Lenzen, F.: Variational Methods in Imaging. AMS, vol. 167. Springer, Cham (2009). https://doi.org/10.1007/978-0-387-69277-7
Zhu, B., Liu, J.Z., Cauley, S.F., Rosen, B.R., Rosen, M.S.: Image reconstruction by domain-transform manifold learning. Nature 555, 487–492 (2018)
Zhu, J.Y., Park, T., Isola, P., Efros, A.A.: Unpaired image-to-image translation using cycle-consistent adversarial networks. arXiv:1703.10593v7, August 2020
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Mukherjee, S., Öktem, O., Schönlieb, CB. (2021). Adversarially Learned Iterative Reconstruction for Imaging Inverse Problems. In: Elmoataz, A., Fadili, J., Quéau, Y., Rabin, J., Simon, L. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2021. Lecture Notes in Computer Science(), vol 12679. Springer, Cham. https://doi.org/10.1007/978-3-030-75549-2_43
Download citation
DOI: https://doi.org/10.1007/978-3-030-75549-2_43
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-75548-5
Online ISBN: 978-3-030-75549-2
eBook Packages: Computer ScienceComputer Science (R0)