Abstract
Robustness of deep learning methods for limited angle tomography is challenged by two major factors: (a) due to insufficient training data the network may not generalize well to unseen data; (b) deep learning methods are sensitive to noise. Thus, generating reconstructed images directly from a neural network appears inadequate. We propose to constrain the reconstructed images to be consistent with the measured projection data, while the unmeasured information is complemented by learning based methods. For this purpose, a data consistent artifact reduction (DCAR) method is introduced: First, a prior image is generated from an initial limited angle reconstruction via deep learning as a substitute for missing information. Afterwards, a conventional iterative reconstruction algorithm is applied, integrating the data consistency in the measured angular range and the prior information in the missing angular range. This ensures data integrity in the measured area, while inaccuracies incorporated by the deep learning prior lie only in areas where no information is acquired. The proposed DCAR method achieves significant image quality improvement: for \(120^\circ \) cone-beam limited angle tomography more than \(10\%\) RMSE reduction in noise-free case and more than \(24\%\) RMSE reduction in noisy case compared with a state-of-the-art U-Net based method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Maier, A., Syben, C., Lasser, T., Riess, C.: A gentle introduction to deep learning in medical image processing. Zeitschrift für Medizinische Physik 29(2), 86–101 (2019)
Wang, G., Ye, J.C., Mueller, K., Fessler, J.A.: Image reconstruction is a new frontier of machine learning. IEEE Trans. Image Process. 37(6), 1289–1296 (2018)
Kang, E., Min, J., Ye, J.C.: A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction. Med. Phys. 44(10), e360–e375 (2017)
Chen, H., et al.: Low-dose CT via convolutional neural network. Biomed. Opt. Express 8(2), 679–694 (2017)
Yang, Q., et al.: Low dose CT image denoising using a generative adversarial network with Wasserstein distance and perceptual loss. IEEE Trans. Med. Imaging 37, 1348–1357 (2018)
Han, Y.S., Yoo, J., Ye, J.C.: Deep residual learning for compressed sensing CT reconstruction via persistent homology analysis. arXiv preprint (2016)
Han, Y., Ye, J.C.: Framing U-Net via deep convolutional framelets: application to sparse-view CT. IEEE Trans. Med. Imaging 37(6), 1418–1429 (2018)
Chen, H., et al.: LEARN: learned experts’ assessment-based reconstruction network for sparse-data CT. IEEE Trans. Med. Imaging 37(6), 1333–1347 (2018)
Gjesteby, L., Yang, Q., Xi, Y., Zhou, Y., Zhang, J., Wang, G.: Deep learning methods to guide CT image reconstruction and reduce metal artifacts. In: Medical Imaging 2017: Physics of Medical Imaging, vol. 10132, p. 101322W. International Society for Optics and Photonics (2017)
Zhang, Y., Yu, H.: Convolutional neural network based metal artifact reduction in X-ray computed tomography. IEEE Trans. Med. Imaging 37(6), 1370–1381 (2018)
Louis, A.K., Törnig, W.: Picture reconstruction from projections in restricted range. Math. Methods Appl. Sci. 2(2), 209–220 (1980)
Huang, Y., et al.: Restoration of missing data in limited angle tomography based on Helgason-Ludwig consistency conditions. Biomed. Phys. Eng. Express 3(3), 035015 (2017)
Sidky, E.Y., Pan, X.: Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys. Med. Biol. 53(17), 4777 (2008)
Chen, Z., Jin, X., Li, L., Wang, G.: A limited-angle CT reconstruction method based on anisotropic TV minimization. Phys. Med. Biol. 58(7), 2119 (2013)
Huang, Y., Taubmann, O., Huang, X., Haase, V., Lauritsch, G., Maier, A.: Scale-space anisotropic total variation for limited angle tomography. IEEE Trans. Radiat. Plasma Med. Sci. 2(4), 307–314 (2018)
Würfl, T., Ghesu, F.C., Christlein, V., Maier, A.: Deep learning computed tomography. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9902, pp. 432–440. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46726-9_50
Zhang, H., et al.: Image prediction for limited-angle tomography via deep learning with convolutional neural network. arXiv preprint (2016)
Gu, J., Ye, J.C.: Multi-scale wavelet domain residual learning for limited-angle CT reconstruction. In: Proceedings of Fully 3D, pp. 443–447 (2017)
Huang, Y., Würfl, T., Breininger, K., Liu, L., Lauritsch, G., Maier, A.: Some investigations on robustness of deep learning in limited angle tomography. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11070, pp. 145–153. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00928-1_17
Würfl, T., et al.: Deep learning computed tomography: learning projection-domain weights from image domain in limited angle problems. IEEE Trans. Med. Imaging 37(6), 1454–1463 (2018)
Bubba, T.A., et al.: Learning the invisible: a hybrid deep learning-shearlet framework for limited angle computed tomography. Inverse Probl. 35(6), 064002 (2019)
Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28
Goodfellow, I.J., Shlens, J., Szegedy, C.: Explaining and harnessing adversarial examples. arXiv preprint (2014)
Szegedy, C., et al.: Intriguing properties of neural networks. arXiv preprint (2013)
Yuan, C., He, P., Zhu, Q., Bhat, R., Li, X.: Adversarial examples: attacks and defenses for deep learning. arXiv preprint (2017)
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? arXiv preprint arXiv:1902.05300 (2019)
Syben, C., et al.: Precision learning: reconstruction filter kernel discretization. In: Noo, F. (ed.) Procs CT Meeting, pp. 386–390 (2018)
Maier, A.K., et al.: Learning with known operators reduces maximum training error bounds. arXiv preprint (2019). Paper conditionally accepted in Nature Machine Intelligence
Riess, C., Berger, M., Wu, H., Manhart, M., Fahrig, R., Maier, A.: TV or not TV? That is the question. In: Proceedings Fully 3D, pp. 341–344 (2013)
Frikel, J.: Sparse regularization in limited angle tomography. Appl. Comput. Harmon. Anal. 34(1), 117–141 (2013)
Huang, G., Liu, Z., Van Der Maaten, L., Weinberger, K.Q.: Densely connected convolutional networks. Proc. CVPR 1(2), 3 (2017)
McCollough, C.H., et al.: Low-dose CT for the detection and classification of metastatic liver lesions: results of the 2016 low dose CT grand challenge. Med. Phys. 44(10), e339–e352 (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Ethics declarations
The concepts and information presented in this paper are based on research and are not commercially available.
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Huang, Y., Preuhs, A., Lauritsch, G., Manhart, M., Huang, X., Maier, A. (2019). Data Consistent Artifact Reduction for Limited Angle Tomography with Deep Learning Prior. In: Knoll, F., Maier, A., Rueckert, D., Ye, J. (eds) Machine Learning for Medical Image Reconstruction. MLMIR 2019. Lecture Notes in Computer Science(), vol 11905. Springer, Cham. https://doi.org/10.1007/978-3-030-33843-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-33843-5_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-33842-8
Online ISBN: 978-3-030-33843-5
eBook Packages: Computer ScienceComputer Science (R0)