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Convergent Data-driven Regularizations for CT Reconstruction
Published 14 Dec 2022 in math.NA, cs.CV, cs.LG, cs.NA, and eess.IV | (2212.07786v2)
Abstract: The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend on the measured data continuously, regularization is needed to re-establish a continuous dependence. In this work, we investigate simple, but yet still provably convergent approaches to learning linear regularization methods from data. More specifically, we analyze two approaches: One generic linear regularization that learns how to manipulate the singular values of the linear operator in an extension of our previous work, and one tailored approach in the Fourier domain that is specific to CT-reconstruction. We prove that such approaches become convergent regularization methods as well as the fact that the reconstructions they provide are typically much smoother than the training data they were trained on. Finally, we compare the spectral as well as the Fourier-based approaches for CT-reconstruction numerically, discuss their advantages and disadvantages and investigate the effect of discretization errors at different resolutions.
- Heinz Werner Engl, Martin Hanke and Andreas Neubauer “Regularization of inverse problems” Dordrecht: Kluwer, 1996
- “Modern regularization methods for inverse problems” In Acta Numerica 27 Cambridge University Press, 2018, pp. 1–111
- “Deep Convolutional Neural Network for Inverse Problems in Imaging” In IEEE Transactions on Image Processing 26.9, 2017, pp. 4509–4522 DOI: 10.1109/TIP.2017.2713099
- Olaf Ronneberger, Philipp Fischer and Thomas Brox “U-Net: Convolutional Networks for Biomedical Image Segmentation” In Medical Image Computing and Computer-Assisted Intervention – MICCAI 2015 Cham: Springer International Publishing, 2015, pp. 234–241
- “Image reconstruction by domain-transform manifold learning” In Nature 555.7697, 2018, pp. 487–492 DOI: 10.1038/nature25988
- Ji He, Yongbo Wang and Jianhua Ma “Radon inversion via deep learning” In IEEE Trans. Med. Imaging 39.6 Institute of ElectricalElectronics Engineers (IEEE), 2020, pp. 2076–2087
- “Learning to Reconstruct Computed Tomography Images Directly From Sinogram Data Under A Variety of Data Acquisition Conditions” In IEEE Transactions on Medical Imaging 38.10, 2019, pp. 2469–2481 DOI: 10.1109/TMI.2019.2910760
- “LEARN: Learned experts’ assessment-based reconstruction network for sparse-data CT” In IEEE Trans. Med. Imaging 37.6, 2018, pp. 1333–1347
- Jinxi Xiang, Yonggui Dong and Yunjie Yang “FISTA-Net: Learning a Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging” In IEEE Transactions on Medical Imaging 40.5, 2021, pp. 1329–1339 DOI: 10.1109/TMI.2021.3054167
- “Learned Primal-Dual Reconstruction” In IEEE Transactions on Medical Imaging 37.6, 2018, pp. 1322–1332 DOI: 10.1109/TMI.2018.2799231
- “Supervised dictionary learning” In NeurIPS, 2008
- Michal Aharon, Michael Elad and Alfred Bruckstein “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation” In IEEE Transactions on signal processing 54.11 IEEE, 2006, pp. 4311–4322
- Stefan Roth and Michael J Black “Fields of experts” In International Journal of Computer Vision 82.2 Springer, 2009, pp. 205–229
- Yunjin Chen, Rene Ranftl and Thomas Pock “Insights into analysis operator learning: From patch-based sparse models to higher order MRFs” In IEEE Transactions on Image Processing 23.3 IEEE, 2014, pp. 1060–1072
- “Total deep variation for linear inverse problems” In CVPR, 2020, pp. 7549–7558
- Michael Moeller, Thomas Mollenhoff and Daniel Cremers “Controlling neural networks via energy dissipation” In ICCV, 2019, pp. 3256–3265
- Yaniv Romano, Michael Elad and Peyman Milanfar “The little engine that could: Regularization by denoising (RED)” In SIAM Journal on Imaging Sciences 10.4 SIAM, 2017, pp. 1804–1844
- “Learning proximal operators: Using denoising networks for regularizing inverse imaging problems” In ICCV, 2017, pp. 1781–1790
- “One network to solve them all–solving linear inverse problems using deep projection models” In ICCV, 2017, pp. 5888–5897
- Dmitry Ulyanov, Andrea Vedaldi and Victor Lempitsky “Deep image prior” In CVPR, 2018, pp. 9446–9454
- “Compressed sensing using generative models” In ICML, 2017, pp. 537–546 PMLR
- “Fast and provable ADMM for learning with generative priors” In NeurIPS, 2019
- Shaojie Bai, J.Zico Kolter and Vladlen Koltun “Deep Equilibrium Models” In Advances in Neural Information Processing Systems 32 Curran Associates, Inc., 2019 URL: https://proceedings.neurips.cc/paper_files/paper/2019/file/01386bd6d8e091c2ab4c7c7de644d37b-Paper.pdf
- Danilo Riccio, Matthias J Ehrhardt and Martin Benning “Regularization of Inverse Problems: Deep Equilibrium Models versus Bilevel Learning” arXiv preprint arXiv:2206.13193
- Brandon Amos, Lei Xu and J Zico Kolter “Input convex neural networks” In ICML, 2017, pp. 146–155 PMLR
- “NETT: Solving inverse problems with deep neural networks” In Inverse Problems 36.6 IOP Publishing, 2020, pp. 065005
- “A data-driven iteratively regularized Landweber iteration” In Numerical Functional Analysis and Optimization 41.10 Taylor & Francis, 2020, pp. 1190–1227
- “Solving inverse problems using data-driven models” In Acta Numerica 28 Cambridge University Press, 2019, pp. 1–174
- Hartmut Bauermeister, Martin Burger and Michael Moeller “Learning Spectral Regularizations for Linear Inverse Problems” In NeurIPS 2020 Workshop on Deep Learning and Inverse Problems
- Julianne Chung, Matthias Chung and Dianne P O’Leary “Designing optimal spectral filters for inverse problems” In SIAM Journal on Scientific Computing 33.6 SIAM, 2011, pp. 3132–3152
- “Low-Dose CT With a Residual Encoder-Decoder Convolutional Neural Network” In IEEE Transactions on Medical Imaging 36.12, 2017, pp. 2524–2535 DOI: 10.1109/TMI.2017.2715284
- Daniel Otero Baguer, Johannes Leuschner and Maximilian Schmidt “Computed tomography reconstruction using deep image prior and learned reconstruction methods” In Inverse Problems 36.9 IOP Publishing, 2020, pp. 094004 DOI: 10.1088/1361-6420/aba415
- “Limited-angle computed tomography with deep image and physics priors” In Scientific Reports 11.1, 2021, pp. 17740 DOI: 10.1038/s41598-021-97226-2
- “Limited-Angle X-Ray CT Reconstruction Using Image Gradient ℓ0subscriptℓ0\ell_{0}roman_ℓ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT-Norm With Dictionary Learning” In IEEE Transactions on Radiation and Plasma Medical Sciences 5.1, 2021, pp. 78–87 DOI: 10.1109/TRPMS.2020.2991887
- “Quantitative Comparison of Deep Learning-Based Image Reconstruction Methods for Low-Dose and Sparse-Angle CT Applications” In Journal of Imaging 7.3, 2021 URL: https://www.mdpi.com/2313-433X/7/3/44
- Minghan Zhang, Sai Gu and Yuhui Shi “The use of deep learning methods in low-dose computed tomography image reconstruction: a systematic review” In Complex & Intelligent Systems, 2022 DOI: 10.1007/s40747-022-00724-7
- Ge Wang, Jong Chul Ye and Bruno De Man “Deep learning for tomographic image reconstruction” In Nature Machine Intelligence 2.12, 2020, pp. 737–748 DOI: 10.1038/s42256-020-00273-z
- “Learning the optimal Tikhonov regularizer for inverse problems” In Advances in Neural Information Processing Systems 34 Inc.: Curran Associates, 2021, pp. 25205–25216
- “A User’s Guide to Optimal Transport” In Modelling and Optimisation of Flows on Networks: Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle Berlin, Heidelberg: Springer Berlin Heidelberg, 2013, pp. 1–155 DOI: 10.1007/978-3-642-32160-3˙1
- “LoDoPaB-CT, a benchmark dataset for low-dose computed tomography reconstruction” In Scientific Data 8.1 Springer ScienceBusiness Media LLC, 2021 DOI: 10.1038/s41597-021-00893-z
- “Some links between continuous and discrete Radon transform” In Medical Imaging 2004: Image Processing 5370 WA, United States: SPIE, 2004, pp. 1961–1971 International Society for OpticsPhotonics DOI: 10.1117/12.533472
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