Abstract
Unrolled neural networks have enabled state-of-the-art reconstruction performance and fast inference times for the accelerated magnetic resonance imaging (MRI) reconstruction task. However, these approaches depend on fully-sampled scans as ground truth data which is either costly or not possible to acquire in many clinical medical imaging applications; hence, reducing dependence on data is desirable. In this work, we propose modeling the proximal operators of unrolled neural networks with scale-equivariant convolutional neural networks in order to improve the data-efficiency and robustness to drifts in scale of the images that might stem from the variability of patient anatomies or change in field-of-view across different MRI scanners. Our approach demonstrates strong improvements over the state-of-the-art unrolled neural networks under the same memory constraints both with and without data augmentations on both in-distribution and out-of-distribution scaled images without significantly increasing the train or inference time.
B. Gunel and A. Sahiner—Equal Contribution.
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References
Aggarwal, H.K., Mani, M.P., Jacob, M.: MoDL: model-based deep learning architecture for inverse problems. IEEE Trans. Med. Imaging 38(2), 394–405 (2018)
Bekkers, E.J., Lafarge, M.W., Veta, M., Eppenhof, K.A.J., Pluim, J.P.W., Duits, R.: Roto-translation covariant convolutional networks for medical image analysis. ArXiv abs/1804.03393 (2018)
Celledoni, E., Ehrhardt, M.J., Etmann, C., Owren, B., Schonlieb, C.B., Sherry, F.: Equivariant neural networks for inverse problems. Inverse Probl. 37, 085006 (2021)
Chen, D., Tachella, J., Davies, M.E.: Equivariant imaging: learning beyond the range space. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 4379–4388 (2021)
Cohen, T., Geiger, M., Köhler, J., Welling, M.: Spherical CNNs. ArXiv abs/1801.10130 (2018)
Cohen, T., Welling, M.: Group equivariant convolutional networks. In: International Conference on Machine Learning, pp. 2990–2999. PMLR (2016)
Darestani, M.Z., Heckel, R.: Accelerated MRI with un-trained neural networks. IEEE Trans. Comput. Imaging 7, 724–733 (2021)
Desai, A.D., et al.: VORTEX: Physics-driven data augmentations for consistency training for robust accelerated MRI reconstruction. In: MIDL (2022)
Desai, A.D., et al.: Noise2Recon: a semi-supervised framework for joint MRI reconstruction and denoising. arXiv preprint arXiv:2110.00075 (2021)
Fabian, Z., Heckel, R., Soltanolkotabi, M.: Data augmentation for deep learning based accelerated MRI reconstruction with limited data. In: International Conference on Machine Learning, pp. 3057–3067. PMLR (2021)
Gunel, B., Mardani, M., Chaudhari, A., Vasanawala, S., Pauly, J.: Weakly supervised MR image reconstruction using untrained neural networks. In: Proceedings of International Society of Magnetic Resonance in Medicine (ISMRM) (2021)
Hadamard, J.: Sur les problèmes aux dérivées partielles et leur signification physique. Princeton Univ. Bull. 49–52 (1902)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
Knoll, F., et al.: Advancing machine learning for MR image reconstruction with an open competition: Overview of the 2019 fastMRI challenge. Magn. Reson. Med. 84(6), 3054–3070 (2020)
Lustig, M., Donoho, D., Pauly, J.M.: Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Resona. Med.: Off. J. Int. Soc. Magn. Reson. Med. 58(6), 1182–1195 (2007)
Lustig, M., Donoho, D.L., Santos, J.M., Pauly, J.M.: Compressed sensing MRI. IEEE Signal Process. Mag. 25(2), 72–82 (2008)
Mardani, M., et al.: Neural proximal gradient descent for compressive imaging. Adv. Neural Inf. Process. Syst. 31 (2018)
Müller, P., Golkov, V., Tomassini, V., Cremers, D.: Rotation-equivariant deep learning for diffusion MRI. ArXiv abs/2102.06942 (2021)
Ong, F., Amin, S., Vasanawala, S., Lustig, M.: Mridata.org: an open archive for sharing MRI raw data. In: Proceedings of International Society for Magnetic Resonance in Medicine, vol. 26, p. 1 (2018)
Ong, F., Lustig, M.: SigPy: a python package for high performance iterative reconstruction. In: Proceedings of the ISMRM 27th Annual Meeting, Montreal, Quebec, Canada, vol. 4819 (2019)
Parikh, N., Boyd, S.: Proximal algorithms. Found. Trends Optim. 1(3), 127–239 (2014)
Pruessmann, K.P., Weiger, M., Scheidegger, M.B., Boesiger, P.: Sense: sensitivity encoding for fast MRI. Magn. Reson. Med.: Off. J. Int. Soc. Magn. Reson. Med. 42(5), 952–962 (1999)
Sahiner, A., Mardani, M., Ozturkler, B., Pilanci, M., Pauly, J.: Convex regularization behind neural reconstruction. arXiv preprint arXiv:2012.05169 (2020)
Sandino, C.M., Cheng, J.Y., Chen, F., Mardani, M., Pauly, J.M., Vasanawala, S.S.: Compressed sensing: from research to clinical practice with deep neural networks: shortening scan times for magnetic resonance imaging. IEEE Signal Process. Mag. 37(1), 117–127 (2020)
Sosnovik, I., Moskalev, A., Smeulders, A.: DISCO: accurate discrete scale convolutions. arXiv preprint arXiv:2106.02733 (2021)
Sosnovik, I., Szmaja, M., Smeulders, A.: Scale-equivariant steerable networks. arXiv preprint arXiv:1910.11093 (2019)
Sriram, A., et al.: End-to-end variational networks for accelerated MRI reconstruction. In: Martel, A.L., et al. (eds.) MICCAI 2020. LNCS, vol. 12262, pp. 64–73. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59713-9_7
Sun, J., Li, H., Xu, Z., et al.: Deep ADMM-net for compressive sensing MRI. Adv. Neural Inf. Process. Syst. 29 (2016)
Vasanawala, S.S., et al.: Practical parallel imaging compressed sensing MRI: summary of two years of experience in accelerating body MRI of pediatric patients. In: 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp. 1039–1043 (2011)
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
Weiler, M., Geiger, M., Welling, M., Boomsma, W., Cohen, T.: 3D steerable CNNs: learning rotationally equivariant features in volumetric data. In: NeurIPS (2018)
Winkels, M., Cohen, T.: 3D G-CNNs for pulmonary nodule detection. ArXiv abs/1804.04656 (2018)
Worrall, D.E., Welling, M.: Deep scale-spaces: equivariance over scale. ArXiv abs/1905.11697 (2019)
Ying, L., Sheng, J.: Joint image reconstruction and sensitivity estimation in SENSE (JSENSE). Magn. Reson. Med.: Off. J. Int. Soc. Magn. Reson. Med. 57(6), 1196–1202 (2007)
Acknowledgements
Beliz Gunel, Arda Sahiner, Shreyas Vasanawala, and John Pauly were supported by NIH R01EB009690 and NIH U01-EB029427-01. Mert Pilanci was partially supported by the National Science Foundation under grants IIS-1838179, ECCS- 2037304, DMS-2134248, and the Army Research Office. Arjun Desai and Akshay Chaudhari were supported by grants R01 AR077604, R01 EB002524, K24 AR062068, and P41 EB015891 from the NIH; the Precision Health and Integrated Diagnostics Seed Grant from Stanford University; National Science Foundation (DGE 1656518, CCF1763315, CCF1563078); DOD – National Science and Engineering Graduate Fellowship (ARO); Stanford Artificial Intelligence in Medicine and Imaging GCP grant; Stanford Human-Centered Artificial Intelligence GCP grant; Microsoft Azure through Stanford Data Science’s Cloud Resources Program; GE Healthcare and Philips.
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Gunel, B. et al. (2022). Scale-Equivariant Unrolled Neural Networks for Data-Efficient Accelerated MRI Reconstruction. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds) Medical Image Computing and Computer Assisted Intervention – MICCAI 2022. MICCAI 2022. Lecture Notes in Computer Science, vol 13436. Springer, Cham. https://doi.org/10.1007/978-3-031-16446-0_70
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