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Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term.
A maximum principle of the Pontryagin type for systems described by nonlinear difference equations
Hubert Halkin · 1966
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Ordinary differential equations
Jack K. Hale · 1980
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Neural networks and the bias/variance dilemma
Stuart Geman, Elie Bienenstock, and René Doursat · 1992
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Nonlinear total variation based noise removal algorithms
Leonid I. Rudin, Stanley Osher, and Emad Fatemi · 1992
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Filtering, segmentation and depth
Mark Nitzberg, David Mumford, and Takahiro Shiota · 1993
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Image recovery via total variation minimization and related problems
Antonin. Chambolle and Pierre-Louis Lions · 1997
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Filters, random fields and maximum entropy (FRAME): Towards a unified theory for texture modeling
Song Chun Zhu, Yingnian Wu, and David Mumford · 1998
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Jinggang Huang and David Mumford · 1999
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A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics
David Martin, Charless Fowlkes, Doron Tal, and Jitendra Malik · 2001
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Euler’s elastica and curvature-based inpainting
Tony F. Chan, Sung Ha Kang, and Jianhong Shen · 2002
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Sobolev spaces
Robert A. Adams and John J. F. Fournier · 2003
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Kostadin Dabov, Alessandro Foi, Vladimir Katkovnik, and Karen Egiazarian · 2007
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Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré · 2008
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Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets
Guang-Hong Chen, Jie Tang, and Shuai Leng · 2008
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Lagrange multiplier approach to variational problems and applications
Kazufumi Ito and Karl Kunisch · 2008
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Fields of Experts
Stefan Roth and Michael J. Black · 2009
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Learning optimized MAP estimates in continuously-valued MRF models
Kegan G. G. Samuel and Marshall F. Tappen · 2009
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Total generalized variation
Kristian Bredies, Karl Kunisch, and Thomas Pock · 2010
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Generic methods for optimization-based modeling
Justin Domke · 2012
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Ordinary differential equations and dynamical systems
Gerald Teschl · 2012
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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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ESPIRiT—an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA
Martin Uecker, Peng Lai, Mark J. Murphy, Patrick Virtue, Michael Elad, John M. Pauly, Shreyas S. Vasanawala, and Michael Lustig · 2014
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ADAM: a method for stochastic optimization
Diederik P. Kingma and Jimmy Lei Ba · 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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The little engine that could: regularization by denoising (RED)
Yaniv Romano, Michael Elad, and Peyman Milanfar · 2017
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Image super-resolution via deep recursive residual network
Ying Tai, Jian Yang, and Xiaoming Liu · 2017
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MemNet: A persistent memory network for image restoration
Ying Tai, Jian Yang, Xiaoming Liu, and Chunyan Xu · 2017
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Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising
Kai Zhang, Wangmeng Zuo, Yunjin Chen, Deyu Meng, and Lei Zhang · 2017
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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
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A look-up table-based ray integration framework for 2-D/3-D forward and back projection in X-ray CT
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Linear functional analysis
Hans Wilhelm Alt · 2016
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An introduction to continuous optimization for imaging
Antonin Chambolle and Thomas Pock · 2016
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Accurate image super-resolution using very deep convolutional networks
Jiwon Kim, Jung Kwon Lee, and Kyoung Mu Lee · 2016
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Non-local color image denoising with convolutional neural networks
Stamatios Lefkimmiatis · 2016
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Inertial proximal alternating linearized minimization (ipalm) for nonconvex and nonsmooth problems
Thomas Pock and Shoham Sabach · 2016
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Trainable nonlinear reaction diffusion: A flexible framework for fast and effective image restoration
Yunjin Chen and Thomas Pock · 2017
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Sungsoo Ha and Klaus Mueller · 2018
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An optimal control approach to deep learning and applications to discrete-weight neural networks
Qianxiao Li and Shuji Hao · 2018
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Adversarial regularizers in inverse problems
Sebastian Lunz, Ozan Öktem, and Carola-Bibiane Schönlieb · 2018
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Neural nearest neighbors networks
Tobias Plötz and Stefan Roth · 2018
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FFDNet: Toward a fast and flexible solution for CNN-based image denoising
Kai Zhang, Wangmeng Zuo, and Lei Zhang · 2018
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Total roto-translational variation
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A mean-field optimal control formulation of deep learning
Weinan E, Jiequn Han, and Qianxiao Li · 2019
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An optimal control approach to early stopping variational methods for image restoration
Alexander Effland, Erich Kobler, Karl Kunisch, and Thomas Pock · 2019
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ODE-inspired network design for single image super-resolution
Xiangyu He, Zitao Mo, Peisong Wang, Yang Liu, Mingyuan Yang, and Jian Cheng · 2019
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FOCNet: A fractional optimal control network for image denoising
Xixi Jia, Sanyang Liu, Xiangchu Feng, and Lei Zhang · 2019
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Making convolutional networks shift-invariant again
Richard Zhang · 2019
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NETT: solving inverse problems with deep neural networks
Housen Li, Johannes Schwab, Stephan Antholzer, and Markus Haltmeier · 2020
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