Abstract
In the past years, there has been a surge of interest in methods to solve inverse problems that are based on neural networks and deep learning. A variety of approaches have been proposed, showing improvements in reconstruction quality over existing methods. Among those, a class of algorithms builds on the well-established variational framework, training a neural network as a regularization functional. Those approaches come with the advantage of a theoretical understanding and a stability theory that is built on existing results for variational regularization. We discuss various approaches for learning a regularization functional, aiming at giving an overview at the multiple directions investigated by the research community.
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References
Adler, J., Öktem, O.: Solving ill-posed inverse problems using iterative deep neural networks. Inverse Probl. 33(12), 124007 (2017)
Adler, J., Öktem, O.: Learned primal-dual reconstruction. IEEE Trans. Med. Imaging 37(6), 1322–1332 (2018)
Aharon, M., Elad, M., Bruckstein, A.: K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54(11), 4311–4322 (2006)
Arridge, S., Maass, P., Öktem, O., Schönlieb, C.-B.: Solving inverse problems using data-driven models. Acta Numer. 28, 1–174 (2019)
Calatroni, L., Cao, C., De Los Reyes, J.C., Schönlieb, C.-B., Valkonen, T.: Bilevel approaches for learning of variational imaging models. RADON Book Series 18 (2012)
Chen, Y., Pock, T., Ranftl, R., Bischof, H.: Revisiting loss-specific training of filter-based MRFs for image restoration. In: German Conference on Pattern Recognition, pp. 271–281. Springer (2013)
Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8), 2080–2095 (2007)
Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems, vol. 375. Springer Science & Business Media, Dordrecht (1996)
Jia, X., Liu, S., Feng, X., Zhang, L.: Focnet: a fractional optimal control network for image denoising. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 6054–6063 (2019)
Jin, K.H., McCann, M., Froustey, E., Unser, M.: Deep convolutional neural network for inverse problems in imaging. IEEE Trans. Image Process. 26(9), 4509–4522 (2017)
Kobler, E., Klatzer, T., Hammernik, K., Pock, T.: Variational networks: connecting variational methods and deep learning. In: German Conference on Pattern Recognition, pp. 281–293. Springer (2017)
Kobler, E., Effland, A., Kunisch, K., Pock, T.: Total deep variation for linear inverse problems (2020)
Kunisch, K., Pock, T.: A bilevel optimization approach for parameter learning in variational models. SIAM J. Imaging Sci. 6(2), 938–983 (2013)
Li, H., Schwab, J., Antholzer, S., Haltmeier, M.: NETT: solving inverse problems with deep neural networks. Inverse Probl. 36, 065005 (2020)
Lunz, S., Öktem, O., Schönlieb, C.-B.: Adversarial regularizers in inverse problems. In: Bengio, S., Wallach, H., Larochelle, H., Grauman, K., Cesa-Bianchi, N., Garnett, R. (eds.) Advances in Neural Information Processing Systems 31, pp. 8507–8516. Curran Associates, Inc., Red Hook (2018)
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)
Obmann, D., Schwab, J., Haltmeier, M.: Deep synthesis regularization of inverse problems. arXiv preprint arXiv:2002.00155 (2020a)
Obmann, D., Nguyen, L., Schwab, J., Haltmeier, M.: Sparse aNETT for solving inverse problems with deep learning. arXiv preprint arXiv:2004.09565 (2020b)
Romano, Y., Elad, M., Milanfar, P.: The little engine that could: regularization by denoising (red). SIAM J. Imaging Sci. 10(4), 1804–1844 (2017)
Ronneberger, O., Fischer, P., Brox, T.: U-net: convolutional networks for biomedical image segmentation. In: International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 234–241. Springer (2015)
Roth, S., Black, M.J.: Fields of experts: a framework for learning image priors. In: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 2, pp. 860–867. IEEE (2005)
Ulyanov, D., Vedaldi, A., Lempitsky, V.: Deep image prior. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9446–9454 (2018)
Xu, Q., Yu, H., Mou, X., Zhang, L., Hsieh, J., Wang, G.: Low-dose x-ray CT reconstruction via dictionary learning. IEEE Trans. Med. Imaging 31(9), 1682–1697 (2012)
Zhang, K., Zuo, W., Chen, Y., Meng, D., Zhang, L.: Beyond a gaussian denoiser: residual learning of deep cnn for image denoising. IEEE Trans. Image Process. 26(7), 3142–3155 (2017)
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Lunz, S. (2023). Learned Regularizers for Inverse Problems. In: Chen, K., Schönlieb, CB., Tai, XC., Younes, L. (eds) Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham. https://doi.org/10.1007/978-3-030-98661-2_68
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DOI: https://doi.org/10.1007/978-3-030-98661-2_68
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