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We propose using the Wasserstein loss for training in inverse problems.
Nonlinear total variation based noise removal algorithms
L.I. Rudin, S. Osher, and E. Fatemi · 1992
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Regularization of inverse problems
H.W. Engl, M. Hanke, and A. Neubauer · 2000
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Mathematical methods in image reconstruction
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Optimal mass transport for registration and warping
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Tomographic image reconstruction using artificial neural networks
P. Paschalis, N. D. Giokaris, A. Karabarbounis, G. K. Loudos, D. Maintas, C. N. Papanicolas, V. Spanoudaki, Ch. Tsoumpas, and E. Stiliaris · 2004
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Optimal transport: old and new
C. Villani · 2008
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Metrics for power spectra: an axiomatic approach
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Natural image denoising with convolutional networks
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Understanding the difficulty of training deep feedforward neural networks
X. Glorot and Y. Bengio · 2010
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Convex analysis and monotone operator theory in Hilbert spaces
H.H. Bauschke and P.L. Combettes · 2011
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Geometric methods for spectral analysis
X. Jiang, Z.-Q. Luo, and T.T. Georgiou · 2012
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Understanding the exploding gradient problem
R. Pascanu, T. Mikolov, and Y. Bengio · 2012
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Image denoising and inpainting with deep neural networks
J. Xie, L. Xu, and E. Chen · 2012
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Sinkhorn distances: Lightspeed computation of optimal transport
M. Cuturi · 2013
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Uncertainty bounds for spectral estimation
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Fast tomographic reconstruction from limited data using artificial neural networks
D. M. Pelt and K. J. Batenburg · 2013
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Magnetic Resonance Imaging: Physical Principles and Sequence Design
R.W. Brown, Y.-C. N. Cheng, E.M. Haacke, M.R. Thompson, and R. Venkatesan · 2014
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Application of the Wasserstein metric to seismic signals
B. Engquist and B.D. Froese · 2014
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Adam: A method for stochastic optimization
D. Kingma and J. Ba · 2014
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MRI distortion: considerations for MRI based radiotherapy treatment planning
A. Walker, G. Liney, P. Metcalfe, and L. Holloway · 2014
Perceptual Losses for Real-Time Style Transfer and Super-Resolution
J. Johnson, A. Alahi, and L. Fei-Fei · 2016
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Generalized Sinkhorn iterations for regularizing inverse problems using optimal mass transport
J. Karlsson and A. Ringh · 2016
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SGDR: stochastic gradient descent with restarts
I. Loshchilov and F. Hutter · 2016
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Fast and flexible X-ray tomography using the ASTRA toolbox
W. van Aarle, W.J. Palenstijn, J. Cant, E. Janssens, F. Bleichrodt, A. Dabravolski, J. De Beenhouwer, K.J. Batenburg, and J. Sijbers · 2016
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Deep learning computed tomography
T. Würfl, F. C. Ghesu, V. Christlein, and A. Maier · 2016
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Iterative Bregman projections for regularized transportation problems
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Unbalanced optimal transport: geometry and Kantorovich formulation
L. Chizat, G. Peyré, B. Schmitzer, and F.-X. Vialard · 2015
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Learning with a Wasserstein loss
C. Frogner, C. Zhang, H. Mobahi, M. Araya, and T.A. Poggio · 2015
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Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
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Mathematics of electron tomography
O. Öktem · 2015
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Tensorflow: Large-scale machine learning on heterogeneous distributed systems
M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. Corrado, A. Davis, J. Dean, M. Devin, et al · 2016
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Deep ADMM-Net for compressive sensing MRI
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ODL - a Python framework for rapid prototyping in inverse problems
J. Adler, H. Kohr, and O. Öktem · 2017
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Learned primal-dual reconstruction
J. Adler and O. Öktem · 2017
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Solving ill-posed inverse problems using iterative deep neural networks
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Deep generative adversarial networks for compressed sensing automates MRI
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Recurrent inference machines for solving inverse problems
P. Putzky and M. Welling · 2017
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Loss functions for image restoration with neural networks
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