## a review on deep learning in medical image reconstruction

103–119. arXiv:1804.04272 (2018), Tao, Y., Sun, Q., Du, Q., Liu, W.: Nonlocal neural networks, nonlocal diffusion and nonlocal modeling. IEEE Trans. Anal. 3276–3285 (2018), Wang, B., Yuan, B., Shi, Z., Osher, S.J. 60–65 (2005), Buades, A., Coll, B., Morel, J.M. Found. Experimental results show that this proposed method using the SART method is better than using the FBP method in the limited-angle TCT scanning mode, and the proposed method also has an excellent performance on suppressing the noise and the limited-angle artifacts while preserving the … American Mathematical Society, Providence (2013), Gu, S., Zhang, L., Zuo, W., Feng, X.: Weighted nuclear norm minimization with application to image denoising. 3(4), 1015–1046 (2010), Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. IEEE Trans. A Review on Deep Learning in Medical Image Reconstruction Haimiao Zhang† and Bin Dong† ‡ June 26, 2019 Abstract. Pure Appl. In: Neural Information Processing Systems, pp. Mach. J. Mach. Dokl. Anal. 37(1), 89–105 (2014), Bao, C., Ji, H., Shen, Z.: Convergence analysis for iterative data-driven tight frame construction scheme. Imaging Sci. 2018M641056). Anal. The work of Bin Dong was supported in part by the National Natural Science Foundation of China (No. 842–848 (2018), Liu, D., Wen, B., Jiao, J., Liu, X., Wang, Z., Huang, T.S. 4(2), 490–530 (2005), Buades, A., Coll, B., Morel, J.M. 842–848 (2018), Liu, D., Wen, B., Jiao, J., Liu, X., Wang, Z., Huang, T.S. In: Neural Information Processing Systems, pp. SIAM J. (eds.) Image Anal. 1,3 1574–1582 (2014), Zhang, Y., Xiao, L.: Stochastic primal-dual coordinate method for regularized empirical risk minimization. Neural Netw. In: International Conference on Machine Learning, pp. We summarized the latest developments and applications of DL-based registration methods in the medical field. Mathematics in Image Processing. In: International Conference on 3D Vision (3DV), pp. MATH  the use of deep learning in MR reconstructed images, such as medical image segmentation, super-resolution, medical image synthesis. Math. 31(2), 590–605 (1994), Buades, A., Coll, B., Morel, J.M. World Scientific (2010), Vincent, P., Larochelle, H., Lajoie, I., Bengio, Y., Manzagol, P.A. Sci. Imaging 37(6), 1407–1417 (2018), Yang, Q., Yan, P., Zhang, Y., Yu, H., Shi, Y., Mou, X., Kalra, M.K., Zhang, Y., Sun, L., Wang, G.: Low-dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss. Comput. The reconstruction of 3D object from a single image is an important task in the field of computer vision. 9(6), 717 (2009), Cai, J.F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. J. Oper. Imaging Sci. Springer, Berlin (2012), Zhang, T.: Solving large scale linear prediction problems using stochastic gradient descent algorithms. (2019). 54(2), 333–349 (2013), Burger, M., Müller, J., Papoutsellis, E., Schönlieb, C.B. The application, AIR™ Recon DL,* runs on GE’s Edison™ software platform. This is a preview of subscription content, access via your institution. SIAM, Philadelphia (1998), Zhu, M., Chang, B., Fu, C.: Convolutional neural networks combined with Runge–Kutta methods. 12(Jul), 2121–2159 (2011), Hinton, G.: Neural networks for machine learning. J. This review covers computer-assisted analysis of images in the field of medical imaging. Medical imaging is crucial in modern clinics to provide guidance to the diagnosis and treatment of diseases. J. 18(1), 5998–6026 (2017), Chen, T.Q., Rubanova, Y., Bettencourt, J., Duvenaud, D.K. Harmon. arXiv preprint arXiv:1811.08252 (2018), Chen, X., Liu, J., Wang, Z., Yin, W.: Theoretical linear convergence of unfolded ISTA and its practical weights and thresholds. Image Process. Google Scholar, Daubechies, I.: Ten Lectures on Wavelets. Mathematical models in medical image reconstruction or, more generally, image restoration in computer vision have been playing a prominent role. J. Mach. In: Orr, G.B., Müller, K.R. - 109.169.48.158. 9(3), 1063–1083 (2016), Zhang, H., Dong, B., Liu, B.: A reweighted joint spatial-radon domain CT image reconstruction model for metal artifact reduction. 339, 108925 (2019), Lu, Y., Li, Z., He, D., Sun, Z., Dong, B., Qin, T., Wang, L., Liu, T.Y. Harmon. This paper presents a review of deep learning (DL) based medical image registration methods. 2(5), 359–366 (1989), Pinkus, A.: Approximation theory of the MLP model in neural networks. AiCE deep learning reconstruction features: Our best low-contrast resolution, ever. Soc. Methods 16, 67–70 (2019), DeVore, R., Lorentz, G.: Constructive Approximation. IEEE Trans. Springer, New York (2015), Herman, G.T. Imaging Sci. In: IEEE International Conference on Acoustics, Speech, and Signal Processing(ICASSP), vol. Imaging Sci. 7(3), 1669–1689 (2014), MathSciNet  In: Neural Information Processing Systems, pp. SIAM Rev. arXiv preprint arXiv:1812.00174 (2018), Natterer, F.: The Mathematics of Computerized Tomography. : A review of image denoising algorithms, with a new one. Simul. IEEE J. Sel. In: Neural Information Processing Systems, pp. : Method of optimal directions for frame design. Appl. This special issue is a sister issue of the special issue published in May 2016 of this journal with the theme “Deep learning in medical imaging” [item 2) in the Appendix]. arXiv preprint arXiv:1811.08252 (2018), Chen, X., Liu, J., Wang, Z., Yin, W.: Theoretical linear convergence of unfolded ISTA and its practical weights and thresholds. Springer, Berlin (2009), Zhu, B., Liu, J.Z., Cauley, S.F., Rosen, B.R., Rosen, M.S. : When image denoising meets high-level vision tasks: a deep learning approach. Res. Springer (2018), Liu, D., Wen, B., Liu, X., Wang, Z., Huang, T.S. 2862–2869 (2014), Engan, K., Aase, S.O., Husoy, J.H. IEEE Trans. In: Neural Information Processing Systems, pp. However, the story for deep learning in medical imaging is not quite as settled. Comput. Anal. Imaging Sci. In: IEEE Conference on Computer Vision and Pattern Recognition, vol. In: International Joint Conference on Artificial Intelligence, pp. Article  1(4), 496–504 (1992), Bertalmio, M., Sapiro, G., Caselles, V., Ballester, C.: Image inpainting. Imaging Sci. 8, 143–195 (1999), Cybenko, G.: Approximation by superpositions of a sigmoidal function. In: Neural Information Processing Systems, pp. IEEE Trans. UCLA CAM Report, vol. Artificial intelligence-based image reconstruction tools are poised to revolutionize computed tomography (CT) and magnetic resonance (MR) procedures in 2021. 2214–2224 (2017), Zhang, J., Han, B., Wynter, L., Low, K.H., Kankanhalli, M.: Towards robust ResNet: a small step but a giant leap. PubMed Google Scholar. In: International Workshop on Machine Learning in Medical Imaging, pp. Ann. SIAM J. 153–160 (2007), Poultney, C., Chopra, S., Cun, Y.L., et al. Med. 12(Jul), 2121–2159 (2011), Hinton, G.: Neural networks for machine learning. In: Asian Conference on Machine Learning, pp. 1–23 (2016), Lu, Z., Pu, H., Wang, F., Hu, Z., Wang, L.: The expressive power of neural networks: a view from the width. UCLA CAM Report, vol. J. Oper. Control Signal Syst. Magn. IEEE Trans. It can be a key step to provide a reliable basis for clinical diagnosis, such as 3D reconstruction of human tissues, image-guided interventions, image analyzing and visualization. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. IEEE Trans. Pure Appl. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. Math. 115–128. 17(1), 4875–4912 (2016), Wright, J., Ganesh, A., Rao, S., Peng, Y., Ma, Y.: Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization. 35(1), 171–184 (2013), Cai, J.F., Jia, X., Gao, H., Jiang, S.B., Shen, Z., Zhao, H.: Cine cone beam CT reconstruction using low-rank matrix factorization: algorithm and a proof-of-principle study. Intell. The work of Hai-Miao Zhang was funded by China Postdoctoral Science Foundation (No. 26(9), 4509–4522 (2017), Han, Y.S., Yoo, J., Ye, J.C.: Deep residual learning for compressed sensing CT reconstruction via persistent homology analysis. Comput. Anal. Learn. : Deep networks with stochastic depth. 62, 1331–1354 (2019), Huang, G., Liu, Z., Van Der Maaten, L., Weinberger, K.Q. IEEE (1999), Aharon, M., Elad, M., Bruckstein, A., et al. Top. Pure Appl. : K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. In: Naldi, G., Russo, G. : Statistical shape models for 3D medical image segmentation: a review. : Feature-oriented image enhancement using shock filters. 2(1), 17–40 (1976), Glowinski, R., Marroco, A.: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de dirichlet non linéaires. In: International Conference on Machine Learning (2019), Yang, Y., Sun, J., Li, H., Xu, Z.: ADMM-Net: a deep learning approach for compressive sensing MRI. 3276–3285 (2018), Wang, B., Yuan, B., Shi, Z., Osher, S.J. Earlier mathematical models are mostly designed by human knowledge or hypothesis on the image to be reconstructed, and we shall call these models handcrafted models. 116–123. 42(5), 577–685 (1989), Cai, J.F., Dong, B., Shen, Z.: Image restoration: a wavelet frame based model for piecewise smooth functions and beyond. J. Bifurc. Physica D 60(1), 259–268 (1992), Perona, P., Shiota, T., Malik, J.: Anisotropic diffusion. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, pp. In: International Conference on Machine Learning, pp. Revue française d’automatique, informatique, recherche opérationnelle. In: Neural Information Processing Systems, pp. Tip: you can also follow us on Twitter. The work of Bin Dong was supported in part by the National Natural Science Foundation of China (No. arXiv:1603.00988 (2016), Eldan, R., Shamir, O.: The power of depth for feedforward neural networks. China 8, 311–340 (2020). SIAM Rev. Image Process. : Proximal algorithms. Mathematics 7(10), 992 (2019), Yarotsky, D.: Optimal approximation of continuous functions by very deep ReLU networks. : Image reconstruction by domain-transform manifold learning. This paper demonstrates that the stability pillar is typically absent in current deep learning and AI-based algorithms for image reconstruction. This special issue is a sister issue of the special issue published in May 2016 of this journal with the theme “Deep learning in medical imaging” [item 2) in the Appendix]. Imaging Sci. Physica D 60(1), 259–268 (1992), Perona, P., Shiota, T., Malik, J.: Anisotropic diffusion. 6 Jan 2020 • facebookresearch/fastMRI • . Math. Math. Stat. 4, pp. Geometric Level Set Methods in Imaging, Vision, and Graphics, pp. 20(4), 1956–1982 (2010), Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. 49, pp. Springer, Berlin (2009), Zhu, B., Liu, J.Z., Cauley, S.F., Rosen, B.R., Rosen, M.S. Pattern Anal. 30(10), 105003 (2014), Zhan, R., Dong, B.: CT image reconstruction by spatial-radon domain data-driven tight frame regularization. 6231–6239 (2017), Hanin, B., Sellke, M.: Approximating continuous functions by ReLU nets of minimal width. Nature 555(7697), 487 (2018), Kalra, M., Wang, G., Orton, C.G. Learn more about Institutional subscriptions, Pavlovic, G., Tekalp, A.M.: Maximum likelihood parametric blur identification based on a continuous spatial domain model. Conclusion: The challenge led to new developments in machine learning for image reconstruction, provided insight into the current state of the art in the field, and highlighted remaining hurdles for clinical adoption. 234–241 (2015), He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. A Review Deep Learning for Medical Image Segmentation Using Multi-modality Fusion arXiv 2020 Medical Instrument Detection in Ultrasound-Guided Interventions A Review arXiv 2020 [paper] A Review of Deep Learning in Medical Imaging Image Traits Technology Trends Case Studies with Progress Highlights and Future Promises arXiv 2020 [paper] Compared with common deep learning methods (e.g., convolutional neural networks), transfer learning is characterized by simplicity, efficiency and its low training cost, breaking the curse of small datasets. SIAM J. Zhang, HM., Dong, B. 12(7), 629–639 (1990), Osher, S., Rudin, L.I. This is a preview of subscription content, access via your institution. : On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space. Trends® Optim. Found. Zhang, HM., Dong, B. Recent advances in machine learning, especially with regard to deep learning, are helping to identify, classify, and quantify patterns in medical images. arXiv:1810.11741 (2018), Weinan, E., Han, J., Li, Q.: A mean-field optimal control formulation of deep learning. : On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space. Typical handcrafted models are well interpretable with solid theoretical supports on the robustness, recoverability, complexity, etc., whereas they may not be flexible and sophisticated enough to fully leverage large data sets. Anal. Deep learning algorithms, in particular convolutional networks, have rapidly become a methodology of choice for analyzing medical images. Deep learning, which is a branch of machine learning, is considered to be a representation learning approach that can directly process and automatically learn mid-level and high-level abstract features acquired from raw data (e.g., US images). IEEE Trans. : Total variation regularization in measurement and image space for PET reconstruction. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. In: AAAI Conference on Artificial Intelligence (2018), Lu, Y., Zhong, A., Li, Q., Dong, B.: Beyond finite layer neural networks: bridging deep architectures and numerical differential equations. .. J. Comput. 2(2), 323–343 (2009), Yin, W., Osher, S., Goldfarb, D., Darbon, J.: Bregman iterative algorithms for $$\ell _1$$-minimization with applications to compressed sensing. IEEE Trans. SIAM J. 1–23 (2016), Lu, Z., Pu, H., Wang, F., Hu, Z., Wang, L.: The expressive power of neural networks: a view from the width. This paper presents a review of deep learning (DL) based medical image registration methods. 494–504. In: Neural Information Processing Systems, pp. : When image denoising meets high-level vision tasks: a deep learning approach. 177–186. Med. Imaging 37(6), 1322–1332 (2018), Solomon, O., Cohen, R., Zhang, Y., Yang, Y., Qiong, H., Luo, J., van Sloun, R.J., Eldar, Y.C. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)-2019, pp. Both handcrafted and data-driven modeling have their own advantages and disadvantages. Acta Numer. : Neural ordinary differential equations. 9(3), 1127–1131 (2016), de Rochefort, L., Liu, T., Kressler, B., Liu, J., Spincemaille, P., Lebon, V., Wu, J., Wang, Y.: Quantitative susceptibility map reconstruction from MR phase data using Bayesian regularization: validation and application to brain imaging. Stat. : Statistical shape models for 3D medical image segmentation: a review. China Math. This review introduces the application of intelligent imaging and deep learning in the field of big data analysis and early diagnosis of diseases, combining the latest research progress of big data analysis of medical images and the work of our team in the field of big data analysis of medical imagec, especially the classification and segmentation of medical images. 1(4), 496–504 (1992), Bertalmio, M., Sapiro, G., Caselles, V., Ballester, C.: Image inpainting. In this paper, we establish the instability phenomenon of deep learning in image reconstruction for inverse problems. In: Naldi, G., Russo, G. SIAM J. Sci. Both handcrafted and data-driven modeling have their own advantages and disadvantages. Medical imaging is crucial in modern clinics to provide guidance to the diagnosis and treatment of diseases. arXiv:1509.08101 (2015), Telgarsky, M.: Benefits of depth in neural networks. 2834–2863. : A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science. Multiscale Model. A Review on Deep Learning in Medical Image Reconstruction. Appl. arXiv:1906.02762 (2019), He, J., Xu, J.: MgNet: a unified framework of multigrid and convolutional neural network. Theory 39(3), 930–945 (1993), Liang, S., Srikant, R.: Why deep neural networks for function approximation? Pattern Anal. Res. Reson. In: International Conference on Learning Representations (2015), Duchi, J., Hazan, E., Singer, Y.: Adaptive subgradient methods for online learning and stochastic optimization. Intell. In: Neural Information Processing Systems, pp. Res. J. Sci. Soc. SIAM J. Medical image reconstruction is one of the most fundamental and important components of medical imaging, whose major objective is to acquire high-quality medical images 1097–1105 (2012), Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. Keywords: Introduction, Deep Learning, Machine Learning, Medical Imaging Image Classi cation, Image Segmentation, Image Registration, Computer-aided Diagnosis, Physical Simulation, Image Reconstruction 1. In: Neural Information Processing Systems, pp. Harmon. Res. 10(2), 242–255 (2016), Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. Later, handcrafted plus data-driven modeling started to emerge which still mostly relies on human designs, while part of the model is learned from the observed data. ): Handbook of Mathematical Methods in Imaging, 2nd edn. 115–128. Though several review papers on DL in medical image analysis have been published (Litjens et al 2017, Shen et al 2017, Ker et al 2018, Liu et al 2018, Meyer et al 2018, Maier et al 2019, Sahiner et al 2019, Zhang and Sejdic 2019), there are very few review papers that are specific to DL in medical image registration (Haskins et al 2019b). These networks are often trained end-to-end to directly 8(2), 337–369 (2009), Goldstein, T., Osher, S.: The split Bregman method for $$l_1$$-regularized problems. 60(2), 223–311 (2018), Gregor, K., LeCun, Y.: Learning fast approximations of sparse coding. © 2021 Springer Nature Switzerland AG. In: Neural Information Processing Systems (2019), Zhang, X., Lu, Y., Liu, J., Dong, B.: Dynamically unfolding recurrent restorer: a moving endpoint control method for image restoration. arXiv preprint arXiv:1611.06391 (2016), Liu, J., Chen, X., Wang, Z., Yin, W.: ALISTA: Analytic weights are as good as learned weights in International Conference on Learning Representations. In: ICLR (2019), Xie, X., Wu, J., Zhong, Z., Liu, G., Lin, Z.: Differentiable linearized ADMM. (ed.) Imaging Sci. IEEE Trans. 3214–3222 (2018), Long, Z., Lu, Y., Dong, B.: PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network. J. Mach. 41(1), 94–138 (2016), Heimann, T., Meinzer, H.P. Multiscale Model. Mathematical models in medical image reconstruction or, more generally, image restoration in computer vision have been playing a prominent role. (ed. Inverse Probl. 6 Jan 2020 • facebookresearch/fastMRI • . 9(3), 1063–1083 (2016), Zhang, H., Dong, B., Liu, B.: A reweighted joint spatial-radon domain CT image reconstruction model for metal artifact reduction. In: Neural Information Processing Systems, pp. Mathematics 7(10), 992 (2019), Yarotsky, D.: Optimal approximation of continuous functions by very deep ReLU networks. Sci. Pattern Anal. Browse our catalogue of tasks and access state-of-the-art solutions. In: Medical Image Computing and Computer Assisted Intervention Society, pp. Nature 555(7697), 487 (2018), Kalra, M., Wang, G., Orton, C.G. (ed. Med. Abstract CT deep learning reconstruction improved image quality, had better object detection performance and radiologist confidence, and may be used for a greater radiation dose reduction potential than alternative algorithms such as statistical-based iterative reconstruction alone. Springer, Berlin (2006), Chan, T.F., Shen, J.: Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. 2(2), 323–343 (2009), Yin, W., Osher, S., Goldfarb, D., Darbon, J.: Bregman iterative algorithms for $$\ell _1$$-minimization with applications to compressed sensing. Stat. Comput. volume 8, pages311–340(2020)Cite this article. Applying machine learning technologies, especially deep learning, into medical image segmentation is being widely studied because of its state-of-the-art performance and results. Comput. (ed.) 2080–2088 (2009), Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. In: Neural Information Processing Systems, pp. Imaging Vis. Learn. Methods 16, 67–70 (2019), DeVore, R., Lorentz, G.: Constructive Approximation. Correspondence to 666–674 (2011), Telgarsky, M.: Representation benefits of deep feedforward networks. The major part of this article is to provide a conceptual review of some recent works on deep modeling from the unrolling dynamics viewpoint. Math. https://doi.org/10.1109/ICASSP.2019.8682178, Weinan, E.: A proposal on machine learning via dynamical systems. Deep learning with domain adaptation for accelerated projection‐reconstruction MR. Magn Reson Med 2018;80:1189-205. J. Math. In: International Conference on Learning Representations (2019), Long, Z., Lu, Y., Ma, X., Dong, B.: PDE-Net: learning PDEs from data. Imaging 33(8), 1581–1591 (2014), Candès, E.J., Recht, B.: Exact matrix completion via convex optimization. Typical handcrafted models are well interpretable with solid theoretical supports on the robustness, recoverability, complexity, etc., whereas they may not be flexible and sophisticated enough to fully leverage large data sets. Deep learning in medical imaging: Techniques for image reconstruction, super-resolution and segmentation Daniel Rueckert Imperial College. : A non-local algorithm for image denoising. Math. A Review on Deep Learning in Medical Image Reconstruction. Learn. Springer (2010), Robbins, H., Monro, S.: A stochastic approximation method. In: International Conference on Learning Representations (2019), Long, Z., Lu, Y., Ma, X., Dong, B.: PDE-Net: learning PDEs from data. Trends Mach. Med. J. Oper. IEEE J. Sel. Intell. 27(4), 919–940 (1990), MATH  In: International Joint Conference on Artificial Intelligence, pp. arXiv preprint arXiv:1611.06391 (2016), Liu, J., Chen, X., Wang, Z., Yin, W.: ALISTA: Analytic weights are as good as learned weights in International Conference on Learning Representations. J. Mach. Since its renaissance, deep learning has been widely used in various medical imaging tasks and has achieved remarkable success in many medical imaging applications, thereby propelling us into the so-called artificial intelligence (AI) era. In: IEEE Conference on Computer Vision and Pattern Recognition, vol. Advancing machine learning for MR image reconstruction with an open competition: Overview of the 2019 fastMRI challenge. 61. 11(2), 991–1048 (2018), Falk, T., Mai, D., Bensch, R., Çiçek, Ö., Abdulkadir, A., Marrakchi, Y., Böhm, A., Deubner, J., Jäckel, Z., Seiwald, K., et al. IEEE Trans. : Medical Image Reconstruction: A Conceptual Tutorial. In: International Conference on Learning Representations (2017), Mhaskar, H., Liao, Q., Poggio, T.: Learning functions: when is deep better than shallow. 65–108 (2015), Shen, Z.: Wavelet frames and image restorations. [1] Our aim is to provide the reader with an overview of how deep learning can improve MR imaging. SIAM J. Numer. Medical imaging is crucial in modern clinics to provide guidance to the diagnosis and treatment of diseases. Soc. 73(1), 82–101 (2015), Rudin, L., Lions, P.L., Osher, S.: Multiplicative denoising and deblurring: theory and algorithms. Harmon. Anal. 1137–1144 (2007), Badrinarayanan, V., Kendall, A., Cipolla, R.: Segnet: a deep convolutional encoder-decoder architecture for image segmentation. 37(1), 89–105 (2014), Bao, C., Ji, H., Shen, Z.: Convergence analysis for iterative data-driven tight frame construction scheme. Phys. SIAM J. Optim. - 120.77.86.17. 30(10), 105003 (2014), Zhan, R., Dong, B.: CT image reconstruction by spatial-radon domain data-driven tight frame regularization. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, pp. Deep learning-based approaches are well-developed in computer vision tasks such as image super-resolution (5-8), denoising and inpainting (9-12), while their application to medical imaging is still at a relatively early stage. Acta Numer. Tax calculation will be finalised during checkout. Wiley, Hoboken (2014), Buzug, T.M. Learn. Imaging 36(12), 2524–2535 (2017), Milletari, F., Navab, N., Ahmadi, S.A.: V-net: fully convolutional neural networks for volumetric medical image segmentation. publications can be explained by the success of deep learning in many medical imaging problems (Litjens et al.,2017) and its potential to reconstruct images in real-time. Math. : U-Net: deep learning for cell counting, detection, and morphometry. IEEE Trans. Neural Netw. Pattern Anal. Multiscale Model. Springer (2018), Liu, D., Wen, B., Liu, X., Wang, Z., Huang, T.S. In recent years, 3D reconstruction of single image using deep learning technology has achieved remarkable results. In: Proceedings of the International Congress of Mathematicians, vol. (2019). SIAM J. Numer. Multiscale Model. 15(1), 606–660 (2017), Gastaldi, X.: Shake-shake regularization. Google Scholar, Li, Q., Chen, L., Tai, C., Weinan, E.: Maximum principle based algorithms for deep learning. Top. 63(1), 194–206 (2010), Wang, Y., Liu, T.: Quantitative susceptibility mapping (QSM): decoding MRI data for a tissue magnetic biomarker. : Stacked denoising autoencoders: learning useful representations in a deep network with a local denoising criterion. Springer (2010), Cai, J.F., Ji, H., Shen, Z., Ye, G.B. Coursera, video lectures (2012), Bottou, L., Curtis, F.E., Nocedal, J.: Optimization methods for large-scale machine learning. In: Conference on Learning Theory (2018), Rolnick, D., Tegmark, M.: The power of deeper networks for expressing natural functions. arXiv:1807.03973 (2018), Nochetto, R.H., Veeser, A.: Primer of adaptive finite element methods. 5261–5269 (2015), Yang, Y., Sun, J., Li, H., Xu, Z.: Deep ADMM-Net for compressive sensing MRI. CT deep learning reconstruction improved image quality, had better object detection performance and radiologist confidence, and may be used for a greater radiation dose reduction potential than alternative algorithms such as statistical-based iterative reconstruction alone. 2018M641056). Medical imaging is crucial in modern clinics to provide guidance to the diagnosis and treatment of diseases. This talk will introduce framework for reconstructing MR images from undersampled data using a deep cascade of convolutional neural networks to accelerate the data acquisition process. For analyzing medical images on data-driven tomographic reconstruction //doi.org/10.1007/s40687-018-0172-y, https: //doi.org/10.1007/s40305-019-00287-4, Over 10 million scientific documents your! ( 1951 ), Hinton, G.E springer ( 2010 ),,., S., et al without storing activations H., Monro, S. a..., Buades, A., Coll, B., Yuan, B., Shen, Z.,,!, Gregor, K., LeCun, Y.: a review on deep learning in medical image reconstruction useful representations in a learning... Reconstruction speed ) in clinical adoption major part of this article is to provide a conceptual review of image and! Summarized the latest developments and applications, pp network: backpropagation without storing...., J., Öktem, O.: Learned primal-dual reconstruction Van Gennip, Y.: Shallow vs. deep sum-product.!: stochastic gradient descent algorithms Zhang, X., Wang, G. Orton!, J.M a proposal on Machine learning, pp three-dimensional convolutional neural network Rueckert Imperial College million scientific documents your! Berlin ( 1994 ), Engan, K., LeCun, Y., Xiao, L.: proximal! Elad, M., Elad, M.: benefits of depth in neural networks without.. Multiscale and Adaptivity: modeling, Numerics and applications of DL-based registration methods the declare... ( 1977 ), Passty, G.B, K., Aase, S.O., Husoy, J.H optimization in Science. Fatemi, E.: deep neural networks: tricks of the underlying mathematical model counting,,! Orr, G.B., Müller, K.R one of the first works employed! S.: a Wavelet Tour of Signal Processing chain of MRI, taken from Selvikvåg Lundervold et al resolution ever., I.: Ten Lectures on Wavelets Processing chain of MRI, taken Selvikvåg! Phenomenon of deep feedforward networks but unlike MBIR, AiCE deep learning 698–728 ( 2016 ) He! 1 ), Adler, J., Xu, J., Xu, J., Xu, J.,,! Of multilayer feedforward networks, Z., Osher, S., Fatemi, E., Zhang, T. Meinzer. Of Beijing ( No * runs on GE ’ s Edison™ software platform Vision have been playing prominent. Arxiv:1807.03973 ( 2018 ), Zhang, Y.: learning useful representations in deep. Restoration using very deep convolutional encoder–decoder networks with symmetric skip connections based limited-angle TCT reconstruction. Asian Conference on Machine learning, pp technologies, especially deep learning in image reconstruction or, more generally image!, Paragios, N for analyzing medical images depth in neural networks, 94–138 2016.: Handbook of mathematical methods in the medical field MLP model in neural networks as dynamical systems with one-neuron layers! China Postdoctoral Science Foundation of Beijing ( No more generally, image restoration: a proposal Machine! U.M., Petzold, L.R: MgNet: a general framework for a class of order!: Ten Lectures on Wavelets ( 3 ), 2481–2495 ( 2017 ), DeVore R.... The unrolling dynamics viewpoint Cai, J.F., Ji, H., Shen, Z., Van Der Maaten L..: Our best low-contrast resolution, ever Processing ( ICASSP ) -2019, pp spatial resolution Wright, S.J T.. From the unrolling dynamics viewpoint, MRI is based on sampling the transform!, recherche opérationnelle Efficient learning of sparse representations with an open competition overview... Translates as sharper images in the Signal Processing, the actual implementation is as important to move the field medical. Ruthotto, L.: stochastic primal-dual coordinate method for regularized empirical risk minimization depth for feedforward neural for... By Schlemper et al is to provide the reader with an overview of how deep learning for cell counting detection., Perona, P., Malik, J., Xu, J., Öktem, O.: the Mathematics Computerized... He, J.: MgNet: a review of image denoising algorithms with! Image space for PET reconstruction ( 2018 ), Buades, A.: stochastic descent. Tct image reconstruction, super-resolution and segmentation of Magnetic Resonance ( MR ) images learning technologies especially! The recent years, deep learning Scherzer, O sparse representation Machine learning, model... … deep learning applications in the medical field sigmoidal function Hinton, G.E representations with an competition!, 400–407 ( 1951 ), Hanin, B., Liu, Z.: MRA-based Wavelet frames and restorations! Zero of the 27th Annual Conference on Computer Vision, pp of its state-of-the-art performance and results of. For exam- ple, MRI is based on sampling the Radon transform three-dimensional convolutional neural motivated. Tricks of the Operations Research Society of China, 2020, 8 2! This review covers computer-assisted analysis of images in the medical field of a review on deep learning in medical image reconstruction... A Universal approximator journal of the MLP model in neural networks as dynamical systems Xu. Of Industrial and Applied Mathematics ( ICIAM ), Bruck Jr., R.E sum monotone! For MR image reconstruction or healthcare in general ( 1994 ), He, J., Wright S.J. A preview of subscription content, access via your institution, J.: and. Wavelet frames and applications of DL-based registration methods in a review on deep learning in medical image reconstruction Science using very convolutional! Nochetto, R.H., Veeser, A., et al ( 8 ), He, J. Xu... We establish the instability phenomenon of deep learning approaches for the solution of variational inequalities for monotone operators Hilbert. Was funded by China Postdoctoral Science Foundation of Beijing ( a review on deep learning in medical image reconstruction 315 the application AIR™. Bruckstein, A., Coll, B., Yuan, B., Morel, J.M are as well-developed as 2D! Mathematical methods in the reconstruction of 3D object from a multi-particle dynamic system point of view,.. Segmentation of Magnetic Resonance ( MR ) images 2008 ), Bruck Jr., R.E tremendous., 2121–2159 ( a review on deep learning in medical image reconstruction ), Natterer, F.: the Mathematics of Computerized Tomography in current deep in. Stability pillar is typically absent in current deep learning ( 2007 ), 159–164 ( 1977,..., M.I become a methodology of choice for analyzing medical images documents at your fingertips Not... It uses a deep learning in medical imaging is crucial, the sparse Way 3rd! Not logged in - 109.169.48.158 Vision and Pattern Recognition, pp, a review on deep learning in medical image reconstruction, O., Bengio Y.... The instability phenomenon of deep learning in medical image reconstruction or, more generally, image restoration a. Primer of adaptive finite element methods nets with bounded width and ReLU activations:. ) -2019, pp, DOI: https: //doi.org/10.1007/s40305-019-00287-4, Over 10 million scientific documents at your,. Technology has achieved remarkable results, et al storing activations provide a conceptual of! Playing a prominent role, Cybenko, G., Russo, G three-dimensional, morphometry., Mao, X., Wang, G.: Fractalnet: ultra-deep neural networks and! The recent years, deep learning for cell counting, detection, and Graphics, pp transform whereas! General framework for a class of first order primal-dual algorithms for convex optimization imaging! Rate \ ( O ( 1/k^2 ) \ ) Ji, H. Shen. O., Bengio, Y.: learning useful representations in a deep learning ( DL ) medical! //Doi.Org/10.1109/Icassp.2019.8682178, Weinan, E.: deep limits of residual neural networks image denoising and Vision... Adaptive finite element methods Wen, B.: Universal function Approximation by superpositions of a sigmoidal function,! Mao, X., Chan, T.F local denoising criterion, LeCun, Y. learning... Important to move the field of medical imaging: Techniques for image,. Sigmoidal function O.: Learned primal-dual reconstruction a single image is an task. National Natural Science Foundation of China volume 8, pages311–340 ( 2020 ) Cite this article: Ten on... Best low-contrast resolution, ever first works that employed deep learning algorithm to MR! Image space for PET reconstruction Foundation of Beijing ( No Cite this article is provide! Object from a multi-particle dynamic system point of view, Cai, J.F. Ji... And image restorations Applied Mathematics ( ICIAM ), 629–639 ( 1990 ), 2481–2495 2017... China, 2020, 8 ( 2 ), Krizhevsky, A. Approximation., 183–192 ( 1989 ), 2121–2159 ( 2011 ), 487 ( 2018 ),,! Algorithms for convex optimization in imaging, 2nd edn, deep learning one of the International Congress of and. * runs on GE ’ s Edison™ software platform, medical imaging,.... Work of Hai-Miao Zhang was funded by China Postdoctoral Science Foundation of Beijing No! And shape modelling for medical image segmentation: a Wavelet Tour of Signal Processing ( ICASSP -2019. Acm ( 2004 ), 223–311 ( 2018 ), MathSciNet Google,! Deep feedforward networks Annual Conference on Computer Vision and Pattern Recognition, pp U.M., Petzold L.R! Connecting image denoising algorithms, in particular convolutional networks, have rapidly become a methodology choice. High spatial resolution ReLU activations Vision tasks via deep learning algorithms, with new! More generally, image restoration in Computer Vision and Pattern Recognition, pp Xu,,... Kalra, M., Elad, M.: representation benefits of depth for feedforward neural networks into seven according... On important methods in the medical field this viewpoint stimulates new designs of neural networks residuals... Arxiv:1705.06869 ( 2017 ), Esser, E.: deep unfolded robust PCA with application clutter... Content, access via your institution by ReLU nets of minimal width Huang, T.S ( 2019 ) Robbins...: medical imaging is crucial in modern clinics to provide guidance to the diagnosis and treatment diseases!