Access the full text.
Sign up today, get DeepDyve free for 14 days.
Yan-jie Zhou, Zhendong Luo (2018)
A Crank–Nicolson collocation spectral method for the two-dimensional telegraph equationsJournal of Inequalities and Applications, 2018
Zhixiang Xue (2020)
A general generative adversarial capsule network for hyperspectral image spectral-spatial classificationRemote Sensing Letters, 11
Özgün Çiçek, A. Abdulkadir, S. Lienkamp, T. Brox, O. Ronneberger (2016)
3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation
Federico Perazzi, J. Pont-Tuset, B. McWilliams, L. Gool, M. Gross, A. Sorkine-Hornung (2016)
A Benchmark Dataset and Evaluation Methodology for Video Object Segmentation2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
O. Ronneberger, P. Fischer, T. Brox (2015)
U-Net: Convolutional Networks for Biomedical Image SegmentationArXiv, abs/1505.04597
S. Mallat (2011)
Group Invariant ScatteringCommunications on Pure and Applied Mathematics, 65
Seoung Oh, Joon-Young Lee, Kalyan Sunkavalli, Seon Kim (2018)
Fast Video Object Segmentation by Reference-Guided Mask Propagation2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition
Diederik Kingma, M. Welling (2013)
Auto-Encoding Variational BayesCoRR, abs/1312.6114
Wenjie Luo, Yujia Li, R. Urtasun, R. Zemel (2016)
Understanding the Effective Receptive Field in Deep Convolutional Neural Networks
Mingyi He, Bo Li, Huahui Chen (2017)
Multi-scale 3D deep convolutional neural network for hyperspectral image classification2017 IEEE International Conference on Image Processing (ICIP)
Ziwei Liu, Ping Luo, Xiaogang Wang, Xiaoou Tang (2014)
Deep Learning Face Attributes in the Wild2015 IEEE International Conference on Computer Vision (ICCV)
W. Press, S. Teukolsky, W. Vettering, B. Flannery (2003)
Numerical Recipes in C++: The Art of Scientific Computing (2nd edn)1 Numerical Recipes Example Book (C++) (2nd edn)2 Numerical Recipes Multi-Language Code CD ROM with LINUX or UNIX Single-Screen License Revised Version3European Journal of Physics, 24
M. Hasanlou, S. Seydi (2018)
Hyperspectral change detection: an experimental comparative studyInternational Journal of Remote Sensing, 39
I. Daubechies (1988)
Orthonormal bases of compactly supported waveletsCommunications on Pure and Applied Mathematics, 41
(2010)
MNIST handwritten digit database
Hyungtae Lee, H. Kwon (2016)
Contextual deep CNN based hyperspectral classification2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS)
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
Tero Karras, Timo Aila, S. Laine, J. Lehtinen (2017)
Progressive Growing of GANs for Improved Quality, Stability, and VariationArXiv, abs/1710.10196
Soheil Kolouri, Charles Martin, G. Rohde (2018)
Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative ModelArXiv, abs/1804.01947
G. Székely, Maria Rizzo (2004)
TESTING FOR EQUAL DISTRIBUTIONS IN HIGH DIMENSION
Tero Karras, S. Laine, Timo Aila (2018)
A Style-Based Generator Architecture for Generative Adversarial Networks2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
Yann LeCun, Yoshua Bengio, Geoffrey Hinton (2015)
Deep LearningNature, 521
Joan Bruna, S. Mallat (2012)
Invariant Scattering Convolution NetworksIEEE transactions on pattern analysis and machine intelligence
Xin Tao, Hongyun Gao, Yi Wang, Xiaoyong Shen, Jue Wang, Jiaya Jia (2018)
Scale-Recurrent Network for Deep Image Deblurring2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition
Yoshua Bengio (2007)
Learning Deep Architectures for AIFound. Trends Mach. Learn., 2
Rui Hou, Chen Chen, M. Shah (2017)
An End-to-end 3D Convolutional Neural Network for Action Detection and Segmentation in VideosArXiv, abs/1712.01111
Edouard Oyallon, Eugene Belilovsky, Sergey Zagoruyko (2017)
Scaling the Scattering Transform: Deep Hybrid Networks2017 IEEE International Conference on Computer Vision (ICCV)
Aidan Gomez, Mengye Ren, R. Urtasun, R. Grosse (2017)
The Reversible Residual Network: Backpropagation Without Storing Activations
Lynton Ardizzone, Carsten Lüth, Jakob Kruse, C. Rother, U. Köthe (2019)
Guided Image Generation with Conditional Invertible Neural NetworksArXiv, abs/1907.02392
B. Peters, J. Granek, E. Haber (2018)
Multi-resolution neural networks for tracking seismic horizons from few training imagesArXiv, abs/1812.11092
Kaiming He, X. Zhang, Shaoqing Ren, Jian Sun (2015)
Deep Residual Learning for Image Recognition2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
B. Hanin (2017)
Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU ActivationsArXiv, abs/1708.02691
S. Fujieda, Kohei Takayama, T. Hachisuka (2017)
Wavelet Convolutional Neural Networks for Texture ClassificationArXiv, abs/1707.07394
A. Gholami, K. Keutzer, G. Biros (2019)
ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEsArXiv, abs/1902.10298
Evan Shelhamer, Jonathan Long, Trevor Darrell (2014)
Fully convolutional networks for semantic segmentation2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
H. Togt (2003)
Publisher's NoteJ. Netw. Comput. Appl., 26
Yann LeCun, Corinna Cortes (2005)
The mnist database of handwritten digits
Gernot Riegler, René Ranftl, M. Rüther, T. Pock, H. Bischof (2015)
Depth Restoration via Joint Training of a Global Regression Model and CNNs
Tim Salimans, I. Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, Xi Chen (2016)
Improved Techniques for Training GANsArXiv, abs/1606.03498
F. Truchetet, O. Laligant (2004)
Wavelets in industrial applications: a review, 5607
Adji Dieng, Francisco Ruiz, D. Blei, Michalis Titsias (2019)
Prescribed Generative Adversarial NetworksArXiv, abs/1910.04302
M. Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, S. Hochreiter (2017)
GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium
Qin Xu, Yong Xiao, Dongyue Wang, B. Luo (2020)
CSA-MSO3DCNN: Multiscale Octave 3D CNN with Channel and Spatial Attention for Hyperspectral Image ClassificationRemote. Sens., 12
T. Chen, Yulia Rubanova, J. Bettencourt, D. Duvenaud (2018)
Neural Ordinary Differential Equations
Jiangyun Li, Binxiu Liang, Yuhao Wang (2020)
A hybrid neural network for hyperspectral image classificationRemote Sensing Letters, 11
K. Hammernik, Teresa Klatzer, Erich Kobler, M. Recht, D. Sodickson, T. Pock, F. Knoll (2017)
Learning a variational network for reconstruction of accelerated MRI dataMagnetic Resonance in Medicine, 79
(2020)
pytorch-fid: FID Score for PyTorch
Zinan Lin, A. Khetan, G. Fanti, Sewoong Oh (2017)
PacGAN: The Power of Two Samples in Generative Adversarial NetworksIEEE Journal on Selected Areas in Information Theory, 1
Akash Srivastava, Lazar Valkov, Chris Russell, Michael Gutmann, Charles Sutton (2017)
VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning
Sifei Liu, Guangyu Zhong, Shalini Mello, Jinwei Gu, Ming-Hsuan Yang, J. Kautz (2018)
Switchable Temporal Propagation Network
S. Caelles, Albert Pumarola, F. Moreno-Noguer, A. Sanfeliu, L. Gool (2019)
Fast video object segmentation with Spatio-Temporal GANsArXiv, abs/1903.12161
B. Dai, U. Seljak (2020)
Sliced Iterative Normalizing Flows
M. Seiler, F. Seiler (1989)
Numerical Recipes in C: The Art of Scientific ComputingRisk Analysis, 9
Du Tran, Lubomir Bourdev, R. Fergus, L. Torresani, Manohar Paluri (2015)
Deep End2End Voxel2Voxel Prediction2016 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)
Christian Etmann, Rihuan Ke, C. Schönlieb (2020)
iUNets: Fully invertible U-Nets with Learnable Up- and DownsamplingArXiv, abs/2005.05220
Sohil Shah, P. Ghosh, L. Davis, T. Goldstein (2018)
Stacked U-Nets: A No-Frills Approach to Natural Image SegmentationArXiv, abs/1804.10343
E Shelhamer, J Long, T Darrell (2017)
Fully convolutional networks for semantic segmentationIEEE Trans. Pattern Anal. Mach. Intell., 39
Vijay Badrinarayanan, Alex Kendall, R. Cipolla (2015)
SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image SegmentationIEEE Transactions on Pattern Analysis and Machine Intelligence, 39
B. Chang, Lili Meng, E. Haber, Lars Ruthotto, David Begert, E. Holtham (2017)
Reversible Architectures for Arbitrarily Deep Residual Neural Networks
Pengju Liu, Hongzhi Zhang, K. Zhang, Liang Lin, W. Zuo (2018)
Multi-level Wavelet-CNN for Image Restoration2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)
Andrew Brock, Jeff Donahue, K. Simonyan (2018)
Large Scale GAN Training for High Fidelity Natural Image SynthesisArXiv, abs/1809.11096
Hengshuang Zhao, Jianping Shi, Xiaojuan Qi, Xiaogang Wang, Jiaya Jia (2016)
Pyramid Scene Parsing Network2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
M. Avendi, A. Kheradvar, H. Jafarkhani (2015)
A combined deep-learning and deformable-model approach to fully automatic segmentation of the left ventricle in cardiac MRIMedical image analysis, 30
J. Jacobsen, A. Smeulders, Edouard Oyallon (2018)
i-RevNet: Deep Invertible NetworksArXiv, abs/1802.07088
Ying Li, Haokui Zhang, Qiang Shen (2017)
Spectral-Spatial Classification of Hyperspectral Imagery with 3D Convolutional Neural NetworkRemote. Sens., 9
Lars Ruthotto, E. Haber (2018)
Deep Neural Networks Motivated by Partial Differential EquationsJournal of Mathematical Imaging and Vision, 62
Laurent Dinh, Jascha Sohl-Dickstein, Samy Bengio (2016)
Density estimation using Real NVPArXiv, abs/1605.08803
A. Krizhevsky, Ilya Sutskever, Geoffrey Hinton (2012)
ImageNet classification with deep convolutional neural networksCommunications of the ACM, 60
A. Krizhevsky (2009)
Learning Multiple Layers of Features from Tiny Images
Jason Yu, K. Derpanis, Marcus Brubaker (2020)
Wavelet Flow: Fast Training of High Resolution Normalizing FlowsArXiv, abs/2010.13821
Convolutional neural networks (CNN) have recently seen tremendous success in various computer vision tasks. However, their application to problems with high dimensional input and output, such as high-resolution image and video segmentation or 3D medical imaging, has been limited by various factors. Primarily, in the training stage, it is necessary to store network activations for back-propagation. In these settings, the memory requirements associated with storing activations can exceed what is feasible with current hardware, especially for problems in 3D. Motivated by the propagation of signals over physical networks, that are governed by the hyperbolic Telegraph equation, in this work we introduce a fully conservative hyperbolic network for problems with high-dimensional input and output. We introduce a coarsening operation that allows completely reversible CNNs by using a learnable discrete wavelet transform and its inverse to both coarsen and interpolate the network state and change the number of channels. We show that fully reversible networks are able to achieve results comparable to the state of the art in 4D time-lapse hyper-spectral image segmentation and full 3D video segmentation, with a much lower memory footprint that is a constant independent of the network depth. We also extend the use of such networks to variational auto-encoders, where optimization begins from an exact recovery and we discover the level of compression through optimization.
Research in the Mathematical Sciences – Springer Journals
Published: Dec 1, 2022
Keywords: Neural networks; Hyperbolic PDE; Wavelets; Auto-encoders
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.