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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.
On linear problems which are not well-posed
Valentin Konstantinovich Ivanov · 1962
Earlier work this paper cites.
Proximité et dualité dans un espace hilbertien
Jean-Jacques Moreau · 1965
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Reverse-time diffusion equation models
Brian D.O. Anderson · 1982
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Nonlinear total variation based noise removal algorithms
Leonid I Rudin, Stanley Osher, and Emad Fatemi · 1992
Earlier work this paper cites.
Nonlinear total variation based noise removal algorithms
Leonid I. Rudin, Stanley Osher, and Emad Fatemi · 1992
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Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
Tianping Chen and Hong Chen · 1995
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Regularization of inverse problems
Heinz Werner Engl and Martin Hanke · 1996
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Convergence rates in forward–backward splitting
George H-G. Chen and R. T. Rockafellar · 1997
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Functions of Bounded Variation and Free Discontinuity Problems
Luigi Ambrosio, Nicola Fusco, and Diego Pallara · 2000
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Training products of experts by minimizing contrastive divergence
Geoffrey E. Hinton · 2002
Earlier work this paper cites.
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
Ingrid Daubechies, Michel Defrise, and Christine De Mol · 2004
Earlier work this paper cites.
A non-local algorithm for image denoising
A. Buades, B. Coll, and J.-M. Morel · 2005
Earlier work this paper cites.
Estimation of non-normalized statistical models by score matching
Aapo Hyvärinen · 2005
Earlier work this paper cites.
Fields of experts: A framework for learning image priors
Stefan Roth and Michael J Black · 2005
Earlier work this paper cites.
Image denoising via sparse and redundant representations over learned dictionaries
Michael Elad and Michal Aharon · 2006
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Optimal spatial adaptation for patch-based image denoising
C. Kervrann and J. Boulanger · 2006
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Image denoising by sparse 3-d transform-domain collaborative filtering
Kostadin Dabov, Alessandro Foi, Vladimir Katkovnik, and Karen Egiazarian · 2007
Earlier work this paper cites.
Linear convergence of iterative soft-thresholding
Kristian Bredies and Dirk A. Lorenz · 2008
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Natural image denoising with convolutional networks
Viren Jain and Sebastian Seung · 2008
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Variational Methods in Imaging
Otmar Scherzer, Markus Grasmair, Harald Grossauer, Markus Haltmeier, and Frank Lenzen · 2008
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
Amir Beck and Marc Teboulle · 2009
Earlier work this paper cites.
Non-local sparse models for image restoration
Julien Mairal, Francis Bach, Jean Ponce, Guillermo Sapiro, and Andrew Zisserman · 2009
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Fields of experts
Stefan Roth and Michael J Black · 2009
Earlier work this paper cites.
Principal neighborhood dictionaries for nonlocal means image denoising
Tolga Tasdizen · 2009
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Optimal transport: old and new
Cédric Villani et al · 2009
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Total generalized variation
Kristian Bredies, Karl Kunisch, and Thomas Pock · 2010
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Learning fast approximations of sparse coding
Karol Gregor and Yann LeCun · 2010
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Inverse problems: a bayesian perspective
Andrew M Stuart · 2010
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Distributed optimization and statistical learning via the alternating direction method of multipliers
Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, and Jonathan Eckstein · 2011
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A first-order primal-dual algorithm for convex problems with applications to imaging
Antonin Chambolle and Thomas Pock · 2011
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Tweedie’s formula and selection bias
Bradley Efron · 2011
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A connection between score matching and denoising autoencoders
Pascal Vincent · 2011
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From learning models of natural image patches to whole image restoration
Daniel Zoran and Yair Weiss · 2011
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A bilevel optimization approach for parameter learning in variational models
Karl Kunisch and Thomas Pock · 2013
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Plug-and-play priors for model based reconstruction
Singanallur V. Venkatakrishnan, Charles A. Bouman, and Brendt Wohlberg · 2013
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What regularized auto-encoders learn from the data-generating distribution
Guillaume Alain and Yoshua Bengio · 2014
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Auto-encoding variational bayes
Diederik P. Kingma and Max Welling · 2014
Earlier work this paper cites.
NICE: non-linear independent components estimation
Laurent Dinh, David Krueger, and Yoshua Bengio · 2015
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Variational inference with normalizing flows
Danilo Rezende and Shakir Mohamed · 2015
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U-net: Convolutional networks for biomedical image segmentation
Olaf Ronneberger, Philipp Fischer, and Thomas Brox · 2015
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Deep unsupervised learning using nonequilibrium thermodynamics
Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli · 2015
Earlier work this paper cites.
Turning a denoiser into a super-resolver using plug and play priors
Alon Brifman, Yaniv Romano, and Michael Elad · 2016
Earlier work this paper cites.
The structure of optimal parameters for image restoration problems
J.C. De Los Reyes, C.-B. Schönlieb, and T. Valkonen · 2016
Earlier work this paper cites.
Unsupervised representation learning with deep convolutional generative adversarial networks
Alec Radford, Luke Metz, and Soumith Chintala · 2016
Earlier work this paper cites.
Plug-and-play priors for bright field electron tomography and sparse interpolation
Suhas Sreehari, S. V. Venkatakrishnan, Brendt Wohlberg, Gregery T. Buzzard, Lawrence F. Drummy, Jeffrey P. Simmons, and Charles A. Bouman · 2016
Earlier work this paper cites.
Learning deep l0 encoders
Zhangyang Wang, Qing Ling, and Thomas Huang · 2016
Earlier work this paper cites.
Deep admm-net for compressive sensing MRI
Yan Yang, Jian Sun, Huibin Li, and Zongben Xu · 2016
Earlier work this paper cites.
Solving ill-posed inverse problems using iterative deep neural networks
Jonas Adler and Ozan Öktem · 2017
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Deep mean-shift priors for image restoration
Siavash Arjomand Bigdeli, Matthias Zwicker, Paolo Favaro, and Meiguang Jin · 2017
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Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Breaking the curse of dimensionality with convex neural networks
Francis Bach · 2017
Earlier work this paper cites.
Image restoration using autoencoding priors
Siavash Arjomand Bigdeli and Matthias Zwicker · 2017
Earlier work this paper cites.
Compressed sensing using generative models
Ashish Bora, Ajil Jalal, Eric Price, and Alexandros G Dimakis · 2017
Earlier work this paper cites.
Plug-and-play admm for image restoration: Fixed-point convergence and applications
Stanley H. Chan, Xiran Wang, and Omar A. Elgendy · 2017
Earlier work this paper cites.
Low-dose ct with a residual encoder-decoder convolutional neural network
Hu Chen, Yi Zhang, Mannudeep K. Kalra, Feng Lin, Yang Chen, Peixi Liao, Jiliu Zhou, and Ge Wang · 2017
Earlier work this paper cites.
Trainable nonlinear reaction diffusion: A flexible framework for fast and effective image restoration
Yunjin Chen and Thomas Pock · 2017
Earlier work this paper cites.
Density estimation using real NVP
Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio · 2017
Earlier work this paper cites.
Improved training of wasserstein GANs
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville · 2017
Earlier work this paper cites.
Image-to-image translation with conditional adversarial networks
Phillip Isola, Jun-Yan Zhu, Tinghui Zhou, and Alexei A. Efros · 2017
Earlier work this paper cites.
Deep convolutional neural network for inverse problems in imaging
Kyong Hwan Jin, Michael T. McCann, Emmanuel Froustey, and Michael Unser · 2017
Earlier work this paper cites.
A plug-and-play priors approach for solving nonlinear imaging inverse problems
Ulugbek S. Kamilov, Hassan Mansour, and Brendt Wohlberg · 2017
Earlier work this paper cites.
A deep convolutional neural network using directional wavelets for low-dose x-ray ct reconstruction
Eunhee Kang, Junhong Min, and Jong Chul Ye · 2017
Earlier work this paper cites.
Convolutional neural networks for inverse problems in imaging: A review
Michael T McCann, Kyong Hwan Jin, and Michael Unser · 2017
Earlier work this paper cites.
Learning proximal operators: Using denoising networks for regularizing inverse imaging problems
Tim Meinhardt, Michael Moller, Caner Hazirbas, and Daniel Cremers · 2017
Earlier work this paper cites.
Recurrent inference machines for solving inverse problems
Patrick Putzky and Max Welling · 2017
Earlier work this paper cites.
One network to solve them all – solving linear inverse problems using deep projection models
J. H. Rick Chang, Chun-Liang Li, Barnabas Poczos, B. V. K. Vijaya Kumar, and Aswin C. Sankaranarayanan · 2017
Earlier work this paper cites.
The little engine that could: Regularization by denoising (red)
Yaniv Romano, Michael Elad, and Peyman Milanfar · 2017
Earlier work this paper cites.
An introduction to data analysis and uncertainty quantification for inverse problems
Luis Tenorio · 2017
Earlier work this paper cites.
Semantic image inpainting with deep generative models
Raymond A. Yeh, Chen Chen, Teck Yian Lim, Alexander G. Schwing, Mark Hasegawa-Johnson, and Minh N. Do · 2017
Earlier work this paper cites.
Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising
Kai Zhang, Wangmeng Zuo, Yunjin Chen, Deyu Meng, and Lei Zhang · 2017
Earlier work this paper cites.
Learning deep cnn denoiser prior for image restoration
Kai Zhang, Wangmeng Zuo, Shuhang Gu, and Lei Zhang · 2017
Earlier work this paper cites.
Learned primal-dual reconstruction
Jonas Adler and Ozan Öktem · 2018
Cited alongside, same era.
Solving bilinear inverse problems using deep generative priors
Muhammad Asim, Fahad Shamshad, and Ali Ahmed · 2018
Cited alongside, same era.
Modeling sparse deviations for compressed sensing using generative models
Manik Dhar, Aditya Grover, and Stefano Ermon · 2018
Cited alongside, same era.
Learning a variational network for reconstruction of accelerated MRI data
Kerstin Hammernik, Teresa Klatzer, Erich Kobler, Michael P. Recht, Daniel K. Sodickson, Thomas Pock, and Florian Knoll · 2018
Cited alongside, same era.
Phase retrieval under a generative prior
Paul Hand, Oscar Leong, and Vlad Voroninski · 2018
Cited alongside, same era.
Deep decoder: Concise image representations from untrained non-convolutional networks
Parameterizing uncertainty by deep invertible networks: An application to reservoir characterization
Gabrio Rizzuti, Ali Siahkoohi, Philipp A. Witte, and Felix J. Herrmann · 2020
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Big in japan: Regularizing networks for solving inverse problems
Johannes Schwab, Stephan Antholzer, and Markus Haltmeier · 2020
Later among the works it cites.
Faster uncertainty quantification for inverse problems with conditional normalizing flows
Ali Siahkoohi, Gabrio Rizzuti, Philipp A Witte, and Felix J Herrmann · 2020
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Sliced score matching: A scalable approach to density and score estimation
Yang Song, Sahaj Garg, Jiaxin Shi, and Stefano Ermon · 2020
Later among the works it cites.
Score-based generative modeling through stochastic differential equations
Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole · 2020
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Reinhard Heckel and Paul Hand · 2018
Cited alongside, same era.
Deep learning for undersampled MRI reconstruction
Chang Min Hyun, Hwa Pyung Kim, Sung Min Lee, Sungchul Lee, and Jin Keun Seo · 2018
Cited alongside, same era.
Glow: Generative flow with invertible 1x1 convolutions
Durk P Kingma and Prafulla Dhariwal · 2018
Cited alongside, same era.
Noise2Noise: Learning image restoration without clean data
Jaakko Lehtinen, Jacob Munkberg, Jon Hasselgren, Samuli Laine, Tero Karras, Miika Aittala, and Timo Aila · 2018
Cited alongside, same era.
Using deep neural networks for inverse problems in imaging: beyond analytical methods
Alice Lucas, Michael Iliadis, Rafael Molina, and Aggelos K Katsaggelos · 2018
Cited alongside, same era.
Adversarial regularizers in inverse problems
Sebastian Lunz, Ozan Öktem, and Carola-Bibiane Schönlieb · 2018
Cited alongside, same era.
prDeep: Robust phase retrieval with a flexible deep network
Christopher Metzler, Phillip Schniter, Ashok Veeraraghavan, and Richard Baraniuk · 2018
Cited alongside, same era.
Later among the works it cites.
Admm-csnet: A deep learning approach for image compressive sensing
Yan Yang, Jian Sun, Huibin Li, and Zongben Xu · 2020
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Ct super-resolution gan constrained by the identical, residual, and cycle learning ensemble (gan-circle)
Chenyu You, Guang Li, Yi Zhang, Xiaoliu Zhang, Hongming Shan, Mengzhou Li, Shenghong Ju, Zhen Zhao, Zhuiyang Zhang, Wenxiang Cong, Michael W. Vannier, Punam K. Saha, Eric A. Hoffman, and Ge Wang · 2020
Later among the works it cites.
A review on deep learning in medical image reconstruction
Hai-Miao Zhang and Bin Dong · 2020
Later among the works it cites.
A review of uncertainty quantification in deep learning: Techniques, applications and challenges
Moloud Abdar, Farhad Pourpanah, Sadiq Hussain, Dana Rezazadegan, Li Liu, Mohammad Ghavamzadeh, Paul Fieguth, Xiaochun Cao, Abbas Khosravi, U Rajendra Acharya, et al · 2021
Later among the works it cites.
Learning the optimal tikhonov regularizer for inverse problems
Giovanni S Alberti, Ernesto De Vito, Matti Lassas, Luca Ratti, and Matteo Santacesaria · 2021
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The modern mathematics of deep learning
Julius Berner, Philipp Grohs, Gitta Kutyniok, and Philipp Petersen · 2021
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Regularization by denoising via fixed-point projection (red-pro)
Regev Cohen, Michael Elad, and Peyman Milanfar · 2021
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Accelerated MRI with un-trained neural networks
Mohammad Zalbagi Darestani and Reinhard Heckel · 2021
Later among the works it cites.
Regularising inverse problems with generative machine learning models
Margaret Duff, Neill DF Campbell, and Matthias J Ehrhardt · 2021
Later among the works it cites.
A residual dense u-net neural network for image denoising
Javier Gurrola-Ramos, Oscar Dalmau, and Teresa E. Alarcón · 2021
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Snips: Solving noisy inverse problems stochastically
Bahjat Kawar, Gregory Vaksman, and Michael Elad · 2021
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A review of the deep learning methods for medical images super resolution problems
Y Li, Bruno Sixou, and F Peyrin · 2021
Later among the works it cites.
Augmented nett regularization of inverse problems
Daniel Obmann, Linh Nguyen, Johannes Schwab, and Markus Haltmeier · 2021
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Solving inverse problems in medical imaging with score-based generative models
Yang Song, Liyue Shen, Lei Xing, and Stefano Ermon · 2021
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Deep probabilistic imaging: Uncertainty quantification and multi-modal solution characterization for computational imaging
He Sun and Katherine L. Bouman · 2021
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Composing normalizing flows for inverse problems
Jay Whang, Erik Lindgren, and Alex Dimakis · 2021
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Fista-net: Learning a fast iterative shrinkage thresholding network for inverse problems in imaging
Jinxi Xiang, Yonggui Dong, and Yunjie Yang · 2021
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Time-dependent deep image prior for dynamic MRI
Jaejun Yoo, Kyong Hwan Jin, Harshit Gupta, Jerome Yerly, Matthias Stuber, and Michael Unser · 2021
Later among the works it cites.
Residual dense network for image restoration
Yulun Zhang, Yapeng Tian, Yu Kong, Bineng Zhong, and Yun Fu · 2021
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Continuous generative neural networks
Giovanni S Alberti, Matteo Santacesaria, and Silvia Sciutto · 2022
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Patchnr: Learning from small data by patch normalizing flow regularization
Fabian Altekrüger, Alexander Denker, Paul Hagemann, Johannes Hertrich, Peter Maass, and Gabriele Steidl · 2022
Later among the works it cites.
Image-to-image regression with distribution-free uncertainty quantification and applications in imaging
Anastasios N Angelopoulos, Amit Pal Kohli, Stephen Bates, Michael Jordan, Jitendra Malik, Thayer Alshaabi, Srigokul Upadhyayula, and Yaniv Romano · 2022
Later among the works it cites.
Regularization theory of the analytic deep prior approach
Clemens Arndt · 2022
Later among the works it cites.
Diffusion posterior sampling for general noisy inverse problems
Hyungjin Chung, Jeongsol Kim, Michael T Mccann, Marc L Klasky, and Jong Chul Ye · 2022
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Improving diffusion models for inverse problems using manifold constraints
Hyungjin Chung, Byeongsu Sim, Dohoon Ryu, and Jong Chul Ye · 2022
Later among the works it cites.
Come-closer-diffuse-faster: Accelerating conditional diffusion models for inverse problems through stochastic contraction
Hyungjin Chung, Byeongsu Sim, and Jong Chul Ye · 2022
Later among the works it cites.
Score-based diffusion models for accelerated MRI
Hyungjin Chung and Jong Chul Ye · 2022
Later among the works it cites.
A proximal markov chain monte carlo method for bayesian inference in imaging inverse problems: When langevin meets moreau
Alain Durmus, Éric Moulines, and Marcelo Pereyra · 2022
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Plug-and-play image reconstruction is a convergent regularization method
Andrea Ebner and Markus Haltmeier · 2022
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Solving inverse problems by joint posterior maximization with autoencoding prior
Mario González, Andrés Almansa, and Pauline Tan · 2022
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A generative variational model for inverse problems in imaging
Andreas Habring and Martin Holler · 2022
Later among the works it cites.
Bayesian imaging with data-driven priors encoded by neural networks
Matthew Holden, Marcelo Pereyra, and Konstantinos C Zygalakis · 2022
Later among the works it cites.
Convergent data-driven regularizations for ct reconstruction
Samira Kabri, Alexander Auras, Danilo Riccio, Hartmut Bauermeister, Martin Benning, Michael Moeller, and Martin Burger · 2022
Later among the works it cites.
Denoising diffusion restoration models
Bahjat Kawar, Michael Elad, Stefano Ermon, and Jiaming Song · 2022
Later among the works it cites.
Total deep variation: A stable regularization method for inverse problems
Erich Kobler, Alexander Effland, Karl Kunisch, and Thomas Pock · 2022
Later among the works it cites.
Two-layer neural networks with values in a banach space
Yury Korolev · 2022
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Error estimates for deeponets: A deep learning framework in infinite dimensions
Samuel Lanthaler, Siddhartha Mishra, and George E Karniadakis · 2022
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Bayesian imaging using plug & play priors: When langevin meets tweedie
Rémi Laumont, Valentin De Bortoli, Andrés Almansa, Julie Delon, Alain Durmus, and Marcelo Pereyra · 2022
Later among the works it cites.
Bayesian uncertainty estimation of learned variational MRI reconstruction
Dominik Narnhofer, Alexander Effland, Erich Kobler, Kerstin Hammernik, Florian Knoll, and Thomas Pock · 2022
Later among the works it cites.
Posterior-variance-based error quantification for inverse problems in imaging
Dominik Narnhofer, Andreas Habring, Martin Holler, and Thomas Pock · 2022
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Exploiting deep generative prior for versatile image restoration and manipulation
Xingang Pan, Xiaohang Zhan, Bo Dai, Dahua Lin, Chen Change Loy, and Ping Luo · 2022
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Untrained neural network priors for inverse imaging problems: A survey
Adnan Qayyum, Inaam Ilahi, Fahad Shamshad, Farid Boussaid, Mohammed Bennamoun, and Junaid Qadir · 2022
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Theoretical perspectives on deep learning methods in inverse problems
Jonathan Scarlett, Reinhard Heckel, Miguel RD Rodrigues, Paul Hand, and Yonina C Eldar · 2022
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Computed tomography reconstruction using generative energy-based priors
Martin Zach, Erich Kobler, and Thomas Pock · 2022
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Plug-and-play image restoration with deep denoiser prior
Kai Zhang, Yawei Li, Wangmeng Zuo, Lei Zhang, Luc Van Gool, and Radu Timofte · 2022
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Latent-space disentanglement with untrained generator networks for the isolation of different motion types in video data
Abdullah Abdullah, Martin Holler, Karl Kunisch, and Malena Sabate Landman · 2023
Closest in time.
Invertible residual networks in the context of regularization theory for linear inverse problems
Clemens Arndt, Alexander Denker, Sören Dittmer, Nick Heilenkötter, Meira Iske, Tobias Kluth, Peter Maass, and Judith Nickel · 2023
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Analysis of generalized iteratively regularized landweber iterations driven by data
Andrea Aspri and Otmar Scherzer · 2023
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Conditional score-based diffusion models for bayesian inference in infinite dimensions
Lorenzo Baldassari, Ali Siahkoohi, Josselin Garnier, Knut Solna, and Maarten V de Hoop · 2023
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Convergence and recovery guarantees of unsupervised neural networks for inverse problems
Nathan Buskulic, Jalal Fadili, and Yvain Quéau · 2023
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Parallel diffusion models of operator and image for blind inverse problems
Hyungjin Chung, Jeongsol Kim, Sehui Kim, and Jong Chul Ye · 2023
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VAEs with structured image covariance applied to compressed sensing MRI
Margaret Duff, Ivor Simpson, Matthias J Ehrhardt, and Neill DF Campbell · 2023
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Joint non-linear MRI inversion with diffusion priors
Moritz Erlacher and Martin Zach · 2023
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A fast data-driven iteratively regularized method with convex penalty for solving ill-posed problems
Guangyu Gao, Bo Han, Zhenwu Fu, and Shanshan Tong · 2023
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Magnetic resonance imaging reconstruction using a deep energy-based model
Yu Guan, Zongjiang Tu, Shanshan Wang, Yuhao Wang, Qiegen Liu, and Dong Liang · 2023
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A note on the regularity of images generated by convolutional neural networks
Andreas Habring and Martin Holler · 2023
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Subgradient langevin methods for sampling from non-smooth potentials
Andreas Habring, Martin Holler, and Thomas Pock · 2023
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Multilevel diffusion: Infinite dimensional score-based diffusion models for image generation
Paul Hagemann, Lars Ruthotto, Gabriele Steidl, and Nicole Tianjiao Yang · 2023
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Data-driven Morozov regularization of inverse problems
Markus Haltmeier, Richard Kowar, and Markus Tiefentaler · 2023
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The devil is in the upsampling: Architectural decisions made simpler for denoising with deep image prior
Yilin Liu, Jiang Li, Yunkui Pang, Dong Nie, and Pew-Thian Yap · 2023
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Bayesian MRI reconstruction with joint uncertainty estimation using diffusion models
Guanxiong Luo, Moritz Blumenthal, Martin Heide, and Martin Uecker · 2023
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Learned reconstruction methods with convergence guarantees: a survey of concepts and applications
Subhadip Mukherjee, Andreas Hauptmann, Ozan Öktem, Marcelo Pereyra, and Carola-Bibiane Schönlieb · 2023
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Gauss–newton method for solving linear inverse problems with neural network coders
Otmar Scherzer, Bernd Hofmann, and Zuhair Nashed · 2023
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Model-based deep learning
Nir Shlezinger, Jay Whang, Yonina C Eldar, and Alexandros G Dimakis · 2023
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K-space and image domain collaborative energy-based model for parallel MRI reconstruction
Zongjiang Tu, Chen Jiang, Yu Guan, Jijun Liu, and Qiegen Liu · 2023
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Stable deep MRI reconstruction using generative priors
Martin Zach, Florian Knoll, and Thomas Pock · 2023
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Explicit diffusion of gaussian mixture model based image priors
Martin Zach, Thomas Pock, Erich Kobler, and Antonin Chambolle · 2023
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