Papers
Topics
Authors
Recent
Search
2000 character limit reached

Neural-network-based regularization methods for inverse problems in imaging

Published 22 Dec 2023 in math.OC and eess.IV | (2312.14849v1)

Abstract: This review provides an introduction to - and overview of - the current state of the art in neural-network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied mathematics and a basic understanding of neural networks to different concepts of applying neural networks for regularizing inverse problems in imaging. Distinguishing features of this review are, among others, an easily accessible introduction to learned generators and learned priors, in particular diffusion models, for inverse problems, and a section focusing explicitly on existing results in function space analysis of neural-network-based approaches in this context.

Authors (2)
Definition Search Book Streamline Icon: https://streamlinehq.com
References (216)
  1. A review of uncertainty quantification in deep learning: Techniques, applications and challenges. Information fusion, 76:243–297, 2021.
  2. Latent-space disentanglement with untrained generator networks for the isolation of different motion types in video data. In International Conference on Scale Space and Variational Methods in Computer Vision, pages 326–338. Springer, 2023.
  3. Solving ill-posed inverse problems using iterative deep neural networks. Inverse Problems, 33(12):124007, 2017.
  4. Learned primal-dual reconstruction. IEEE Transactions on Medical Imaging, 37(6):1322–1332, 2018.
  5. What regularized auto-encoders learn from the data-generating distribution. The Journal of Machine Learning Research, 15(1):3563–3593, 2014.
  6. Learning the optimal tikhonov regularizer for inverse problems. Advances in Neural Information Processing Systems, 34:25205–25216, 2021.
  7. Continuous generative neural networks. arXiv preprint arXiv:2205.14627, 2022.
  8. Patchnr: Learning from small data by patch normalizing flow regularization. arXiv preprint arXiv:2205.12021, 2022.
  9. Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs, 2000.
  10. Brian D.O. Anderson. Reverse-time diffusion equation models. Stochastic Processes and their Applications, 12(3):313–326, 1982.
  11. Image-to-image regression with distribution-free uncertainty quantification and applications in imaging. In International Conference on Machine Learning, pages 717–730. PMLR, 2022.
  12. NETT regularization for compressed sensing photoacoustic tomography. In Alexander A. Oraevsky and Lihong V. Wang, editors, Photons Plus Ultrasound: Imaging and Sensing 2019, volume 10878, page 108783B. International Society for Optics and Photonics, SPIE, 2019.
  13. Deep mean-shift priors for image restoration. In I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017.
  14. Wasserstein generative adversarial networks. In Doina Precup and Yee Whye Teh, editors, Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pages 214–223. PMLR, 2017.
  15. Clemens Arndt. Regularization theory of the analytic deep prior approach. Inverse Problems, 38(11):115005, 2022.
  16. Invertible residual networks in the context of regularization theory for linear inverse problems. arXiv preprint arXiv:2306.01335, 2023.
  17. Solving inverse problems using data-driven models. Acta Numerica, 28:1–174, 2019.
  18. Invertible generative models for inverse problems: mitigating representation error and dataset bias. In Hal Daumé III and Aarti Singh, editors, Proceedings of the 37th International Conference on Machine Learning, volume 119 of Proceedings of Machine Learning Research, pages 399–409. PMLR, 2020.
  19. Solving bilinear inverse problems using deep generative priors. CoRR, abs/1802.04073, 3(4):8, 2018.
  20. Blind image deconvolution using deep generative priors. IEEE Transactions on Computational Imaging, 6:1493–1506, 2020.
  21. A data-driven iteratively regularized landweber iteration. Numerical Functional Analysis and Optimization, 41(10):1190–1227, 2020.
  22. Data driven regularization by projection. Inverse Problems, 36(12):125009, 2020.
  23. Analysis of generalized iteratively regularized landweber iterations driven by data. arXiv preprint arXiv:2312.03337, 2023.
  24. Francis Bach. Breaking the curse of dimensionality with convex neural networks. The Journal of Machine Learning Research, 18(1):629–681, 2017.
  25. Deep learning methods for solving linear inverse problems: Research directions and paradigms. Signal Processing, 177:107729, 2020.
  26. Conditional score-based diffusion models for bayesian inference in infinite dimensions. arXiv preprint arXiv:2305.19147, 2023.
  27. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1):183–202, 2009.
  28. The modern mathematics of deep learning. arXiv preprint arXiv:2105.04026, pages 86–114, 2021.
  29. Image restoration using autoencoding priors. arXiv preprint arXiv:1703.09964, 2017.
  30. Compressed sensing using generative models. In International conference on machine learning, pages 537–546. PMLR, 2017.
  31. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3(1):1–122, 2011.
  32. Higher-order total variation approaches and generalisations. Inverse Problems. Topical Review, 36(12):123001, 2020.
  33. Total generalized variation. SIAM Journal on Imaging Sciences, 3(3):492–526, 2010.
  34. Linear convergence of iterative soft-thresholding. Journal of Fourier Analysis and Applications, 14(5):813–837, 2008.
  35. Turning a denoiser into a super-resolver using plug and play priors. In 2016 IEEE International Conference on Image Processing (ICIP), pages 1404–1408, 2016.
  36. A non-local algorithm for image denoising. In 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), volume 2, pages 60–65 vol. 2, 2005.
  37. Convergence and recovery guarantees of unsupervised neural networks for inverse problems. arXiv preprint arXiv:2309.12128, 2023.
  38. A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, 40(1):120–145, 2011.
  39. Plug-and-play admm for image restoration: Fixed-point convergence and applications. IEEE Transactions on Computational Imaging, 3(1):84–98, 2017.
  40. George H-G. Chen and R. T. Rockafellar. Convergence rates in forward–backward splitting. SIAM Journal on Optimization, 7(2):421–444, 1997.
  41. Low-dose ct with a residual encoder-decoder convolutional neural network. IEEE Transactions on Medical Imaging, 36(12):2524–2535, 2017.
  42. Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems. IEEE transactions on neural networks, 6(4):911–917, 1995.
  43. Trainable nonlinear reaction diffusion: A flexible framework for fast and effective image restoration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 39(6):1256–1272, 2017.
  44. A bayesian perspective on the deep image prior. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5443–5451, 2019.
  45. Parallel diffusion models of operator and image for blind inverse problems. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 6059–6069, 2023.
  46. Diffusion posterior sampling for general noisy inverse problems. arXiv preprint arXiv:2209.14687, 2022.
  47. Improving diffusion models for inverse problems using manifold constraints. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 25683–25696. Curran Associates, Inc., 2022.
  48. Come-closer-diffuse-faster: Accelerating conditional diffusion models for inverse problems through stochastic contraction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 12413–12422, 2022.
  49. Score-based diffusion models for accelerated MRI. Medical Image Analysis, 80:102479, 2022.
  50. Regularization by denoising via fixed-point projection (red-pro). SIAM Journal on Imaging Sciences, 14(3):1374–1406, 2021.
  51. Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Transactions on Image Processing, 16(8):2080–2095, 2007.
  52. Accelerated MRI with un-trained neural networks. IEEE Transactions on Computational Imaging, 7:724–733, 2021.
  53. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on Pure and Applied Mathematics, 57(11):1413–1457, 2004.
  54. The structure of optimal parameters for image restoration problems. Journal of Mathematical Analysis and Applications, 434(1):464–500, 2016.
  55. Modeling sparse deviations for compressed sensing using generative models. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 1214–1223. PMLR, 2018.
  56. NICE: non-linear independent components estimation. In Yoshua Bengio and Yann LeCun, editors, 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Workshop Track Proceedings, 2015.
  57. Density estimation using real NVP. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. OpenReview.net, 2017.
  58. Regularization by architecture: A deep prior approach for inverse problems. Journal of Mathematical Imaging and Vision, 62:456–470, 2020.
  59. Denoising prior driven deep neural network for image restoration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 41(10):2305–2318, 2019.
  60. Regularising inverse problems with generative machine learning models. arXiv preprint arXiv:2107.11191, 2021.
  61. VAEs with structured image covariance applied to compressed sensing MRI. Physics in Medicine & Biology, 68(16):165008, 2023.
  62. Analysis of langevin monte carlo via convex optimization. The Journal of Machine Learning Research, 20(1):2666–2711, 2019.
  63. High-dimensional Bayesian inference via the unadjusted Langevin algorithm. Bernoulli, 25(4A):2854 – 2882, 2019.
  64. A proximal markov chain monte carlo method for bayesian inference in imaging inverse problems: When langevin meets moreau. SIAM Review, 64(4):991–1028, 2022.
  65. Plug-and-play image reconstruction is a convergent regularization method. arXiv preprint arXiv:2212.06881, 2022.
  66. Bradley Efron. Tweedie’s formula and selection bias. Journal of the American Statistical Association, 106(496):1602–1614, 2011. PMID: 22505788.
  67. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image Processing, 15(12):3736–3745, 2006.
  68. Regularization of inverse problems, volume 375. Springer Science & Business Media, 1996.
  69. Joint non-linear MRI inversion with diffusion priors. arXiv preprint arXiv:2310.14842, 2023.
  70. A fast data-driven iteratively regularized method with convex penalty for solving ill-posed problems. SIAM Journal on Imaging Sciences, 16(2):640–670, 2023.
  71. Solving inverse problems by joint posterior maximization with autoencoding prior. SIAM Journal on Imaging Sciences, 15(2):822–859, 2022.
  72. Generative adversarial nets. In Z. Ghahramani, M. Welling, C. Cortes, N. Lawrence, and K.Q. Weinberger, editors, Advances in Neural Information Processing Systems, volume 27. Curran Associates, Inc., 2014.
  73. Learning fast approximations of sparse coding. In Proceedings of the 27th International Conference on International Conference on Machine Learning, ICML’10, page 399–406, Madison, WI, USA, 2010. Omnipress.
  74. Magnetic resonance imaging reconstruction using a deep energy-based model. NMR in Biomedicine, 36(3):e4848, 2023.
  75. Improved training of wasserstein GANs. In I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017.
  76. Agem: Solving linear inverse problems via deep priors and sampling. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019.
  77. A residual dense u-net neural network for image denoising. IEEE Access, 9:31742–31754, 2021.
  78. A generative variational model for inverse problems in imaging. SIAM Journal on Mathematics of Data Science, 4(1):306–335, 2022.
  79. A note on the regularity of images generated by convolutional neural networks. SIAM Journal on Mathematics of Data Science, 5(3):670–692, 2023.
  80. Subgradient langevin methods for sampling from non-smooth potentials. arXiv preprint arXiv:2308.01417, 2023.
  81. Multilevel diffusion: Infinite dimensional score-based diffusion models for image generation. arXiv preprint arXiv:2303.04772, 2023.
  82. Data-driven Morozov regularization of inverse problems. arXiv preprint arXiv:2310.14290, 2023.
  83. Learning a variational network for reconstruction of accelerated MRI data. Magnetic Resonance in Medicine, 79(6):3055–3071, 2018.
  84. Phase retrieval under a generative prior. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018.
  85. Parseval proximal neural networks. Journal of Fourier Analysis and Applications, 26:1–31, 2020.
  86. Optimizing a parameterized plug-and-play admm for iterative low-dose ct reconstruction. IEEE Transactions on Medical Imaging, 38(2):371–382, 2019.
  87. Reinhard Heckel. Regularizing linear inverse problems with convolutional neural networks. arXiv preprint arXiv:1907.03100, 2019.
  88. Deep decoder: Concise image representations from untrained non-convolutional networks. arXiv preprint arXiv:1810.03982, 2018.
  89. Denoising and regularization via exploiting the structural bias of convolutional generators. arXiv preprint arXiv:1910.14634, 2019.
  90. Compressive sensing with un-trained neural networks: Gradient descent finds a smooth approximation. In International Conference on Machine Learning, pages 4149–4158. PMLR, 2020.
  91. Noise2inverse: Self-supervised deep convolutional denoising for tomography. IEEE Transactions on Computational Imaging, 6:1320–1335, 2020.
  92. Geoffrey E. Hinton. Training products of experts by minimizing contrastive divergence. Neural Computation, 14(8):1771–1800, 2002.
  93. Denoising diffusion probabilistic models. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 6840–6851. Curran Associates, Inc., 2020.
  94. Bayesian imaging with data-driven priors encoded by neural networks. SIAM Journal on Imaging Sciences, 15(2):892–924, 2022.
  95. Acceleration of red via vector extrapolation. Journal of Visual Communication and Image Representation, 63:102575, 2019.
  96. Deep learning for undersampled MRI reconstruction. Physics in Medicine & Biology, 63(13):135007, 2018.
  97. Aapo Hyvärinen. Estimation of non-normalized statistical models by score matching. Journal of Machine Learning Research, 6(24):695–709, 2005.
  98. Image-to-image translation with conditional adversarial networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.
  99. Valentin Konstantinovich Ivanov. On linear problems which are not well-posed. Doklady Akademii Nauk SSSR, 145(2):270–272, 1962.
  100. Algorithmic guarantees for inverse imaging with untrained network priors. Advances in neural information processing systems, 32, 2019.
  101. Natural image denoising with convolutional networks. In D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, editors, Advances in Neural Information Processing Systems, volume 21. Curran Associates, Inc., 2008.
  102. Deep convolutional neural network for inverse problems in imaging. IEEE Transactions on Image Processing, 26(9):4509–4522, 2017.
  103. Convergent data-driven regularizations for ct reconstruction. arXiv preprint arXiv:2212.07786, 2022.
  104. A plug-and-play priors approach for solving nonlinear imaging inverse problems. IEEE Signal Processing Letters, 24(12):1872–1876, 2017.
  105. A deep convolutional neural network using directional wavelets for low-dose x-ray ct reconstruction. Medical Physics, 44(10):e360–e375, 2017.
  106. Invertible convolutional flow. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019.
  107. Denoising diffusion restoration models. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 23593–23606. Curran Associates, Inc., 2022.
  108. Snips: Solving noisy inverse problems stochastically. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P.S. Liang, and J. Wortman Vaughan, editors, Advances in Neural Information Processing Systems, volume 34, pages 21757–21769. Curran Associates, Inc., 2021.
  109. C. Kervrann and J. Boulanger. Optimal spatial adaptation for patch-based image denoising. IEEE Transactions on Image Processing, 15(10):2866–2878, 2006.
  110. Auto-encoding variational bayes. In Yoshua Bengio and Yann LeCun, editors, 2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings, 2014.
  111. Glow: Generative flow with invertible 1x1 convolutions. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018.
  112. fastMRI: A publicly available raw k-space and DICOM dataset of knee images for accelerated MR image reconstruction using machine learning. Radiology: Artificial Intelligence, 2(1):e190007, 2020.
  113. Total deep variation for linear inverse problems. In Proceedings of the IEEE/CVF Conference on computer vision and pattern recognition, pages 7549–7558, 2020.
  114. Total deep variation: A stable regularization method for inverse problems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(12):9163–9180, 2022.
  115. Yury Korolev. Two-layer neural networks with values in a banach space. SIAM Journal on Mathematical Analysis, 54(6):6358–6389, 2022.
  116. A bilevel optimization approach for parameter learning in variational models. SIAM Journal on Imaging Sciences, 6(2):938–983, 2013.
  117. Error estimates for deeponets: A deep learning framework in infinite dimensions. Transactions of Mathematics and Its Applications, 6(1):tnac001, 2022.
  118. Bayesian imaging using plug & play priors: When langevin meets tweedie. SIAM Journal on Imaging Sciences, 15(2):701–737, 2022.
  119. Noise2Noise: Learning image restoration without clean data. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 2965–2974. PMLR, 2018.
  120. Nett: solving inverse problems with deep neural networks. Inverse Problems, 36(6):065005, 2020.
  121. A review of the deep learning methods for medical images super resolution problems. IRBM, 42(2):120–133, 2021.
  122. Image restoration using total variation regularized deep image prior. In ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 7715–7719. Ieee, 2019.
  123. The devil is in the upsampling: Architectural decisions made simpler for denoising with deep image prior. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 12408–12417, 2023.
  124. Using deep neural networks for inverse problems in imaging: beyond analytical methods. IEEE Signal Processing Magazine, 35(1):20–36, 2018.
  125. Adversarial regularizers in inverse problems. In S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018.
  126. Bayesian MRI reconstruction with joint uncertainty estimation using diffusion models. Magnetic Resonance in Medicine, 90(1):295–311, 2023.
  127. Non-local sparse models for image restoration. In 2009 IEEE 12th International Conference on Computer Vision, pages 2272–2279, 2009.
  128. Deepred: Deep image prior powered by red. In Proceedings of the IEEE/CVF International Conference on Computer Vision Workshops, pages 0–0, 2019.
  129. Convolutional neural networks for inverse problems in imaging: A review. IEEE Signal Processing Magazine, 34(6):85–95, 2017.
  130. Learning proximal operators: Using denoising networks for regularizing inverse imaging problems. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2017.
  131. prDeep: Robust phase retrieval with a flexible deep network. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 3501–3510. PMLR, 2018.
  132. Jean-Jacques Moreau. Proximité et dualité dans un espace hilbertien. Bulletin de la Société mathématique de France, 93:273–299, 1965.
  133. Stochastic seismic waveform inversion using generative adversarial networks as a geological prior. Mathematical Geosciences, 52(1):53–79, 2020.
  134. Learned convex regularizers for inverse problems. arXiv preprint arXiv:2008.02839, 2020.
  135. Learned reconstruction methods with convergence guarantees: a survey of concepts and applications. IEEE Signal Processing Magazine, 40(1):164–182, 2023.
  136. Bayesian uncertainty estimation of learned variational MRI reconstruction. IEEE Transactions on Medical Imaging, 41(2):279–291, 2022.
  137. Posterior-variance-based error quantification for inverse problems in imaging. arXiv preprint arXiv:2212.12499, 2022.
  138. Augmented nett regularization of inverse problems. Journal of Physics Communications, 5(10):105002, 2021.
  139. Deep synthesis network for regularizing inverse problems. Inverse Problems, 37(1):015005, 2020.
  140. Deep learning techniques for inverse problems in imaging. IEEE Journal on Selected Areas in Information Theory, 1(1):39–56, 2020.
  141. Exploiting deep generative prior for versatile image restoration and manipulation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(11):7474–7489, 2022.
  142. Improving tomographic reconstruction from limited data using mixed-scale dense convolutional neural networks. Journal of Imaging, 4(11), 2018.
  143. Recurrent inference machines for solving inverse problems. arXiv preprint arXiv:1706.04008, 2017.
  144. Untrained neural network priors for inverse imaging problems: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022.
  145. Compressed sensing MRI reconstruction using a generative adversarial network with a cyclic loss. IEEE Transactions on Medical Imaging, 37(6):1488–1497, 2018.
  146. Unsupervised representation learning with deep convolutional generative adversarial networks. In Yoshua Bengio and Yann LeCun, editors, 4th International Conference on Learning Representations, ICLR 2016, San Juan, Puerto Rico, May 2-4, 2016, Conference Track Proceedings, 2016.
  147. Gan-based projector for faster recovery with convergence guarantees in linear inverse problems. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2019.
  148. Denoising score-matching for uncertainty quantification in inverse problems. arXiv preprint arXiv:2011.08698, 2020.
  149. Regularization by denoising: Clarifications and new interpretations. IEEE Transactions on Computational Imaging, 5(1):52–67, 2019.
  150. Variational inference with normalizing flows. In Francis Bach and David Blei, editors, Proceedings of the 32nd International Conference on Machine Learning, volume 37 of Proceedings of Machine Learning Research, pages 1530–1538, Lille, France, 2015. PMLR.
  151. One network to solve them all – solving linear inverse problems using deep projection models. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2017.
  152. Parameterizing uncertainty by deep invertible networks: An application to reservoir characterization. In SEG International Exposition and Annual Meeting, page D031S057R006, 2020.
  153. The little engine that could: Regularization by denoising (red). SIAM Journal on Imaging Sciences, 10(4):1804–1844, 2017.
  154. Conformalized quantile regression. Advances in neural information processing systems, 32, 2019.
  155. U-net: Convolutional networks for biomedical image segmentation. In International Conference on Medical image computing and computer-assisted intervention, pages 234–241. Springer, 2015.
  156. Fields of experts: A framework for learning image priors. In 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), volume 2, pages 860–867. IEEE, 2005.
  157. Fields of experts. International Journal of Computer Vision, 82(2):205–229, 2009.
  158. Nonlinear total variation based noise removal algorithms. Physica D: nonlinear phenomena, 60(1-4):259–268, 1992.
  159. Nonlinear total variation based noise removal algorithms. Physica D, 60(1–4):259–268, 1992.
  160. Plug-and-play methods provably converge with properly trained denoisers. In Kamalika Chaudhuri and Ruslan Salakhutdinov, editors, Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pages 5546–5557. PMLR, 2019.
  161. Theoretical perspectives on deep learning methods in inverse problems. IEEE journal on selected areas in information theory, 3(3):433–453, 2022.
  162. Variational Methods in Imaging, volume 167. Springer Science & Business Media, 2008.
  163. Gauss–newton method for solving linear inverse problems with neural network coders. Sampling Theory, Signal Processing, and Data Analysis, 21(2):25, 2023.
  164. A deep cascade of convolutional neural networks for dynamic mr image reconstruction. IEEE Transactions on Medical Imaging, 37(2):491–503, 2018.
  165. Bayesian deep learning for accelerated mr image reconstruction. In Machine Learning for Medical Image Reconstruction: First International Workshop, MLMIR 2018, Held in Conjunction with MICCAI 2018, Granada, Spain, September 16, 2018, Proceedings 1, pages 64–71. Springer, 2018.
  166. Deep null space learning for inverse problems: convergence analysis and rates. Inverse Problems, 35(2):025008, 2019.
  167. Big in japan: Regularizing networks for solving inverse problems. Journal of mathematical imaging and vision, 62(3):445–455, 2020.
  168. Self-supervised learning of inverse problem solvers in medical imaging. In Qian Wang, Fausto Milletari, Hien V. Nguyen, Shadi Albarqouni, M. Jorge Cardoso, Nicola Rieke, Ziyue Xu, Konstantinos Kamnitsas, Vishal Patel, Badri Roysam, Steve Jiang, Kevin Zhou, Khoa Luu, and Ngan Le, editors, Domain Adaptation and Representation Transfer and Medical Image Learning with Less Labels and Imperfect Data, pages 111–119, Cham, 2019. Springer International Publishing.
  169. A learning-based method for solving ill-posed nonlinear inverse problems: A simulation study of lung eit. SIAM Journal on Imaging Sciences, 12(3):1275–1295, 2019.
  170. Solving linear inverse problems using gan priors: An algorithm with provable guarantees. In 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 4609–4613, 2018.
  171. Model-based deep learning. Proceedings of the IEEE, 2023.
  172. Faster uncertainty quantification for inverse problems with conditional normalizing flows. arXiv preprint arXiv:2007.07985, 2020.
  173. Deep unsupervised learning using nonequilibrium thermodynamics. In Francis Bach and David Blei, editors, Proceedings of the 32nd International Conference on Machine Learning, volume 37 of Proceedings of Machine Learning Research, pages 2256–2265, Lille, France, 2015. PMLR.
  174. Generative modeling by estimating gradients of the data distribution. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019.
  175. Sliced score matching: A scalable approach to density and score estimation. In Ryan P. Adams and Vibhav Gogate, editors, Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, volume 115 of Proceedings of Machine Learning Research, pages 574–584. PMLR, 2020.
  176. Solving inverse problems in medical imaging with score-based generative models. arXiv preprint arXiv:2111.08005, 2021.
  177. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456, 2020.
  178. Plug-and-play priors for bright field electron tomography and sparse interpolation. IEEE Transactions on Computational Imaging, 2(4):408–423, 2016.
  179. Andrew M Stuart. Inverse problems: a bayesian perspective. Acta numerica, 19:451–559, 2010.
  180. He Sun and Katherine L. Bouman. Deep probabilistic imaging: Uncertainty quantification and multi-modal solution characterization for computational imaging. Proceedings of the AAAI Conference on Artificial Intelligence, 35(3):2628–2637, 2021.
  181. Block coordinate regularization by denoising. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019.
  182. An online plug-and-play algorithm for regularized image reconstruction. IEEE Transactions on Computational Imaging, 5(3):395–408, 2019.
  183. Tolga Tasdizen. Principal neighborhood dictionaries for nonlocal means image denoising. IEEE Transactions on Image Processing, 18(12):2649–2660, 2009.
  184. Luis Tenorio. An introduction to data analysis and uncertainty quantification for inverse problems. SIAM, 2017.
  185. Enhanced cnn for image denoising. CAAI Transactions on Intelligence Technology, 4(1):17–23, 2019.
  186. Image restoration by iterative denoising and backward projections. IEEE Transactions on Image Processing, 28(3):1220–1234, 2019.
  187. K-space and image domain collaborative energy-based model for parallel MRI reconstruction. Magnetic Resonance Imaging, 99:110–122, 2023.
  188. Deep image prior. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 9446–9454, 2018.
  189. Compressed sensing with deep image prior and learned regularization. arXiv preprint arXiv:1806.06438, 2018.
  190. Plug-and-play priors for model based reconstruction. In 2013 IEEE Global Conference on Signal and Information Processing, pages 945–948, 2013.
  191. Cédric Villani et al. Optimal transport: old and new, volume 338. Springer, 2009.
  192. Pascal Vincent. A connection between score matching and denoising autoencoders. Neural Computation, 23(7):1661–1674, 2011.
  193. Learning deep l0 encoders. Proceedings of the AAAI Conference on Artificial Intelligence, 30(1), 2016.
  194. Composing normalizing flows for inverse problems. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, pages 11158–11169. PMLR, 2021.
  195. Learning likelihoods with conditional normalizing flows. arXiv preprint arXiv:1912.00042, 2019.
  196. Online regularization by denoising with applications to phase retrieval. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, 2019.
  197. Fista-net: Learning a fast iterative shrinkage thresholding network for inverse problems in imaging. IEEE Transactions on Medical Imaging, 40(5):1329–1339, 2021.
  198. Dagan: Deep de-aliasing generative adversarial networks for fast compressed sensing MRI reconstruction. IEEE Transactions on Medical Imaging, 37(6):1310–1321, 2018.
  199. Low-dose ct image denoising using a generative adversarial network with wasserstein distance and perceptual loss. IEEE Transactions on Medical Imaging, 37(6):1348–1357, 2018.
  200. Deep admm-net for compressive sensing MRI. In D. Lee, M. Sugiyama, U. Luxburg, I. Guyon, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 29. Curran Associates, Inc., 2016.
  201. Admm-csnet: A deep learning approach for image compressive sensing. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42(3):521–538, 2020.
  202. Deep residual learning for model-based iterative ct reconstruction using plug-and-play framework. In 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 6668–6672, 2018.
  203. Semantic image inpainting with deep generative models. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.
  204. Time-dependent deep image prior for dynamic MRI. IEEE Transactions on Medical Imaging, 40(12):3337–3348, 2021.
  205. Ct super-resolution gan constrained by the identical, residual, and cycle learning ensemble (gan-circle). IEEE Transactions on Medical Imaging, 39(1):188–203, 2020.
  206. Stable deep MRI reconstruction using generative priors. IEEE Transactions on Medical Imaging, pages 1–1, 2023.
  207. Computed tomography reconstruction using generative energy-based priors. arXiv preprint arXiv:2203.12658, 2022.
  208. Explicit diffusion of gaussian mixture model based image priors. In Luca Calatroni, Marco Donatelli, Serena Morigi, Marco Prato, and Matteo Santacesaria, editors, Scale Space and Variational Methods in Computer Vision, pages 3–15, Cham, 2023. Springer International Publishing.
  209. A review on deep learning in medical image reconstruction. Journal of the Operations Research Society of China, 8:311–340, 2020.
  210. Ista-net: Interpretable optimization-inspired deep network for image compressive sensing. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2018.
  211. Plug-and-play image restoration with deep denoiser prior. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(10):6360–6376, 2022.
  212. Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising. IEEE Transactions on Image Processing, 26(7):3142–3155, 2017.
  213. Learning deep cnn denoiser prior for image restoration. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017.
  214. Residual dense network for image restoration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43(7):2480–2495, 2021.
  215. Image reconstruction by domain-transform manifold learning. Nature, 555(7697):487–492, 2018.
  216. From learning models of natural image patches to whole image restoration. In 2011 International Conference on Computer Vision, pages 479–486, 2011.
Citations (1)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 1 tweet with 1 like about this paper.

Sign Up for Free