The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Learning a variational network for reconstruction of accelerated MRI data
Open accessAbstract
Purpose: To allow fast and high‐quality reconstruction of clinical accelerated multi‐coil MR data by learning a variational network that combines the mathematical structure of variational models with deep learning. Theory and Methods: Generalized compressed sensing reconstruction formulated as a variational model is embedded in an unrolled gradient descent scheme. All parameters of this formulation, including the prior model defined by filter kernels and activation functions as well as the data term weights, are learned during an offline training procedure. The learned model can then be applied online to previously unseen data. Results: The variational network approach is evaluated on a clinical knee imaging protocol for different acceleration factors and sampling patterns using retrospectively and prospectively undersampled data. The variational network reconstructions outperform standard reconstruction algorithms, verified by quantitative error measures and a clinical reader study for regular sampling and acceleration factor 4. Conclusion: Variational network reconstructions preserve the natural appearance of MR images as well as pathologies that were not included in the training data set. Due to its high computational performance, that is, reconstruction time of 193 ms on a single graphics card, and the omission of parameter tuning once the network is trained, this new approach to image reconstruction can easily be integrated into clinical workflow. Magn Reson Med 79:3055–3071, 2018. © 2017 International Society for Magnetic Resonance in Medicine.
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LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
Image quality assessment: from error visibility to structural similarity
Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.819861 · Cited by 57,892
Sparse MRI: The application of compressed sensing for rapid MR imaging
Lustig, M., Donoho, D., & Pauly, J. M. (2007) · Magnetic Resonance in Medicine · doi:10.1002/mrm.21391 · Cited by 6,952
Emergence of simple-cell receptive field properties by learning a sparse code for natural images
Olshausen, B. A., & Field, D. J. (1996) · Nature · doi:10.1038/381607a0 · Cited by 5,694
Flownet: Learning optical flow with convolutional networks
Dosovitskiy, A., Fischer, P., Ilg, E., Hausser, P., Hazirbas, C., Golkov, V., Smagt, P. V. D., Cremers, D., & Brox, T. (2015) · 2015 IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2015.316 · Cited by 4,313
Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs
Chen, L.-C., Papandreou, G., Kokkinos, I., Murphy, K., & Yuille, A. L. (2014) · arXiv · doi:10.48550/arxiv.1412.7062 · Cited by 4,213
Daugman, J. G. (1985) · Journal of the Optical Society of America A · doi:10.1364/josaa.2.001160 · Cited by 3,219
Automatic Segmentation of MR Brain Images With a Convolutional Neural Network
Moeskops, P., Viergever, M. A., Mendrik, A. M., de Vries, L. S., Benders, M. J. N. L., & Isgum, I. (2016) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2016.2548501 · Cited by 861 · cited 1×
“In medical imaging, deep learning has also been applied to areas like segmentation (7, 8), q-space image processing (9), and skull stripping (10).”
MethodDeep convolutional neural networks for multi-modality isointense infant brain image segmentation
Zhang, W., Li, R., Deng, H., Wang, L., Lin, W., Ji, S., & Shen, D. (2015) · NeuroImage · doi:10.1016/j.neuroimage.2014.12.061 · Cited by 817
Deep MRI brain extraction: A 3D convolutional neural network for skull stripping
Kleesiek, J., Urban, G., Hubert, A., Schwarz, D., Maier-Hein, K., Bendszus, M., & Biller, A. (2016) · NeuroImage · doi:10.1016/j.neuroimage.2016.01.024 · Cited by 505 · cited 1×
“In medical imaging, deep learning has also been applied to areas like segmentation (7, 8), q-space image processing (9), and skull stripping (10).”
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All-optical machine learning using diffractive deep neural networks
Lin, X., Rivenson, Y., Yardimci, N. T., Veli, M., Luo, Y., Jarrahi, M., & Ozcan, A. (2018) · Science · doi:10.1126/science.aat8084 · Cited by 2,568
Image reconstruction by domain-transform manifold learning
Zhu, B., Liu, J. Z., Cauley, S. F., Rosen, B. R., & Rosen, M. S. (2018) · Nature · doi:10.1038/nature25988 · Cited by 1,694
Yang, G., Yu, S., Dong, H., Slabaugh, G., Dragotti, P. L., Ye, X., Liu, F., Arridge, S., Keegan, J., Guo, Y., et al. (2018) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2017.2785879 · Cited by 1,081
Deep learning for tomographic image reconstruction
Wang, G., Ye, J. C., & De Man, B. (2020) · Nature Machine Intelligence · doi:10.1038/s42256-020-00273-z · Cited by 531
fastMRI: An Open Dataset and Benchmarks for Accelerated MRI
Žbontar, J., Knöll, F., Sriram, A., Murrell, T., Huang, Z., Muckley, M. J., Defazio, A., Stern, R., Johnson, P., Bruno, M. T., et al. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1811.08839 · Cited by 528
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Metadata
- Authors
- Hammernik, K., Klatzer, T., Kobler, E., Recht, M. P., Sodickson, D. K., Pock, T., & Knoll, F.
- Venue
- Magnetic Resonance in Medicine
- Publisher
- Wiley
- Published
- 2017-11-08
- Volume
- 79
- Issue
- 6
- Pages
- 3055-3071
- ISSN
- 0740-3194 (ISSN-L)
- 1522-2594
- OpenAlex
- W2604388535
- Cited by
- 1,713
- References
- 10
- FWCI
- 78.76
- Type
- journal article
- Language
- en
- Open access
- green
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