Abstract
Compressed Sensing MRI (CS-MRI) has shown promise in reconstructing under-sampled MR images, offering the potential to reduce scan times. Classical techniques minimize a regularized least-squares cost function using an expensive iterative optimization procedure. Recently, deep learning models have been developed that model the iterative nature of classical techniques by unrolling iterations in a neural network. While exhibiting superior performance, these methods require large quantities of ground-truth images and have shown to be non-robust to unseen data. In this paper, we explore a novel strategy to train an unrolled reconstruction network in an unsupervised fashion by adopting a loss function widely-used in classical optimization schemes. We demonstrate that this strategy achieves lower loss and is computationally cheap compared to classical optimization solvers while also exhibiting superior robustness compared to supervised models. Code is available at https://github.com/alanqrwang/HQSNet.
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Notes
- 1.
In this paper, we assume a single coil acquisition.
- 2.
For forward models that do not permit an analytical solution of Eq. (7b) (e.g. multi-coil MRI), one can replace the data-consistency layer with an iterative optimization scheme (e.g. conjugate gradient as in [1]). In addition, the iteration-specific weights \(\theta _k\) in Eq. (7a) can be replaced by a shared set of weights \(\theta \), which enforces the model to learn a global regularization prior for all iterations.
- 3.
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 (2019)
Antun, V., Renna, F., Poon, C., Adcock, B., Hansen, A.C.: On instabilities of deep learning in image reconstruction - does AI come at a cost? (2019)
Bahadir, C.D., Wang, A.Q., Dalca, A.V., Sabuncu, M.R.: Deep-learning-based optimization of the under-sampling pattern in MRI. IEEE Trans. Comput. Imaging 6, 1139–1152 (2020)
Balakrishnan, G., Zhao, A., Sabuncu, M.R., Guttag, J., Dalca, A.V.: VoxelMorph: a learning framework for deformable medical image registration. IEEE Trans. Med. Imaging 38(8), 1788–1800 (2019)
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imging Sci. 2(1), 183–202 (2009)
Bergstra, J., Yamins, D., Cox, D.D.: Making a science of model search: hyperparameter optimization in hundreds of dimensions for vision architectures. In: Proceedings of the 30th International Conference on International Conference on Machine Learning, ICML 2013, vol. 28. pp. I-115–I-123. JMLR.org
Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120–145 (2011)
Chauffert, N., Ciuciu, P., Weiss, P.: Variable density compressed sensing in MRI. theoretical vs heuristic sampling strategies. In: 2013 IEEE 10th International Symposium on Biomedical Imaging, April 2013
Cheng, K., Du, J., Zhou, H., Zhao, D., Qin, H.: Image super-resolution based on half quadratic splitting. Infrared Phys. Technol. 105, 103193 (2020)
Combettes, P.L., Pesquet, J.C.: Proximal splitting methods in signal processing. In: Bauschke, H., Burachik, R., Combettes, P., Elser, V., Luke, D., Wolkowicz, H. (eds.) Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp. 185–212. Springer, New York (2011). https://doi.org/10.1007/978-1-4419-9569-8_10
Cremer, C., Li, X., Duvenaud, D.: Inference suboptimality in variational autoencoders (2018)
Dalca, A.V., Guttag, J., Sabuncu, M.R.: Anatomical priors in convolutional networks for unsupervised biomedical segmentation. In: The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2018)
Daubechies, I., Defrise, M., Mol, C.D.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57, 1413–1457 (2004)
Dong, W., Wang, P., Yin, W., Shi, G., Wu, F., Lu, X.: Denoising prior driven deep neural network for image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 41(10), 2305–2318 (2018)
Figueiredo, M.A.T., Nowak, R.D.: An EM algorithm for wavelet-based image restoration. IEEE Trans. Image Process. 12(8), 906–916 (2003)
Geethanath, S., et al.: Compressed sensing MRI: a review. Crit. Rev. Biomed. Eng. 41(3), 183–204 (2013)
Geman, D., Yang, C.: Nonlinear image recovery with half-quadratic regularization. IEEE Trans. Image Process. 4(7), 932–946 (1995)
Gershman, S.J., Goodman, N.D.: Amortized inference in probabilistic reasoning. In: CogSci (2014)
Hammernik, K., et al.: Learning a variational network for reconstruction of accelerated MRI data. Magn. Reson. Med. 79(6), 3055–3071 (2017)
Hu, Y., Jacob, M.: Higher degree total variation (HDTV) regularization for image recovery. IEEE Trans. Image Process. 21(5), 2559–2571 (2012)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization (2014)
Lee, D., Yoo, J., Ye, J.C.: Deep residual learning for compressed sensing MRI. In: 2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017), pp. 15–18, April 2017
Liang, D., Cheng, J., Ke, Z., Ying, L.: Deep MRI reconstruction: unrolled optimization algorithms meet neural networks (2019)
Lustig, M., Donoho, D., Pauly, J.M.: Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58(6), 1182–1195 (2007)
Mardani, M., et al.: Neural proximal gradient descent for compressive imaging (2018)
Marino, J., Yue, Y., Mandt, S.: Iterative amortized inference (2018)
Nikolova, M., Ng, M.K.: Analysis of half-quadratic minimization methods for signal and image recovery. SIAM J. Sci. Comput. 27(3), 937–966 (2005)
Ravishankar, S., Bresler, Y.: MR image reconstruction from highly undersampled k-space data by dictionary learning. IEEE Trans. Med. Imaging 30(5), 1028–1041 (2011)
Ravishankar, S., Ye, J.C., Fessler, J.A.: Image reconstruction: from sparsity to data-adaptive methods and machine learning. Proc. IEEE 108(1), 86–109 (2020)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1–4), 259–268 (1992)
Schlemper, J., Caballero, J., Hajnal, J.V., Price, A., Rueckert, D.: A deep cascade of convolutional neural networks for MR image reconstruction. In: Niethammer, M., et al. (eds.) IPMI 2017. LNCS, vol. 10265, pp. 647–658. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59050-9_51
Shu, R., Bui, H.H., Zhao, S., Kochenderfer, M.J., Ermon, S.: Amortized inference regularization (2018)
Tezcan, K.C., Baumgartner, C.F., Luechinger, R., Pruessmann, K.P., Konukoglu, E.: MR image reconstruction using deep density priors. IEEE Trans. Med. Imaging 38(7), 1633–1642 (2019)
Wang, S., et al.: Accelerating magnetic resonance imaging via deep learning. In: 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI), pp. 514–517, April 2016
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Imaging Process. 13(4), 600–612 (2004)
Yang, Y., Sun, J., Li, H., Xu, Z.: ADMM-Net: a deep learning approach for compressive sensing MRI (2017)
Ye, N., Roosta-Khorasani, F., Cui, T.: Optimization methods for inverse problems. 2017 MATRIX Annals. MBS, vol. 2, pp. 121–140. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04161-8_9
Zbontar, J., et al.: fastMRI: an open dataset and benchmarks for accelerated MRI (2018)
Acknowledgements
This research was funded by NIH grants R01LM012719, R01AG053949; and, NSF CAREER 1748377, and NSF NeuroNex Grant1707312.
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Wang, A.Q., Dalca, A.V., Sabuncu, M.R. (2020). Neural Network-Based Reconstruction in Compressed Sensing MRI Without Fully-Sampled Training Data. In: Deeba, F., Johnson, P., Würfl, T., Ye, J.C. (eds) Machine Learning for Medical Image Reconstruction. MLMIR 2020. Lecture Notes in Computer Science(), vol 12450. Springer, Cham. https://doi.org/10.1007/978-3-030-61598-7_3
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