Abstract
Tomographic image reconstruction is relevant for many medical imaging modalities including X-ray, ultrasound (US) computed tomography (CT) and photoacoustics, for which the access to full angular range tomographic projections might be not available in clinical practice due to physical or time constraints. Reconstruction from incomplete data in low signal-to-noise ratio regime is a challenging and ill-posed inverse problem that usually leads to unsatisfactory image quality. While informative image priors may be learned using generic deep neural network architectures, the artefacts caused by an ill-conditioned design matrix often have global spatial support and cannot be efficiently filtered out by means of convolutions. In this paper we propose to learn an inverse mapping in an end-to-end fashion via unrolling optimization iterations of a prototypical reconstruction algorithm. We herein introduce a network architecture that performs filtering jointly in both sinogram and spatial domains. To efficiently train such deep network we propose a novel regularization approach based on deep exponential weighting. Experiments on US and X-ray CT data show that our proposed method is qualitatively and quantitatively superior to conventional non-linear reconstruction methods as well as state-of-the-art deep networks for image reconstruction. Fast inference time of the proposed algorithm allows for sophisticated reconstructions in real-time critical settings, demonstrated with US SoS imaging of an ex vivo bovine phantom.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adler, J., Öktem, O.: Learned primal-dual reconstruction. IEEE Trans. Med. Imaging 37(6), 1322–1332 (2018)
Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends ML 3(1), 1–122 (2011)
Cheng, A., et al.: Deep learning image reconstruction method for limited-angle ultrasound tomography in prostate cancer. In: Proceedings of SPIE Medical Imaging, p. 1095516 (2019)
Hammernik, K., et al.: Learning a variational network for reconstruction of accelerated MRI data. MRM 79(6), 3055–3071 (2018)
Hammernik, K., Würfl, T., Pock, T., Maier, A.: A deep learning architecture for limited-angle computed tomography reconstruction. Bildverarbeitung für die Medizin 2017. INFORMAT, pp. 92–97. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54345-0_25
Knoll, F., Bredies, K., Pock, T., Stollberger, R.: Second order total generalized variation (TGV) for MRI. MRM 65(2), 480–491 (2011)
Landweber, L.: An iteration formula for Fredholm integral equations of the first kind. Am. J. Math. 73(3), 615–624 (1951)
Lin, H., Azuma, T., Unlu, M.B., Takagi, S.: Evaluation of adjoint methods in photoacoustic tomography with under-sampled sensors. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11070, pp. 73–81. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00928-1_9
Liu, Y., Lew, M.S.: Learning relaxed deep supervision for better edge detection. In: CVPR, pp. 231–240 (2016)
Maier, A., Syben, C., Lasser, T., Riess, C.: A gentle introduction to deep learning in medical image processing. Zeitschrift für Medizinische Physik 29, 86–101 (2019)
Paige, C.C., Saunders, M.A.: LSQR: an algorithm for sparse linear equations and sparse least squares. ACM TOMS 8(1), 43–71 (1982)
Rau, R., Unal, O., Schweizer, D., Vishnevskiy, V., Goksel, O.: Attenuation imaging with pulse-echo ultrasound based on an acoustic reflector. In: MICCAI (2016, accepted). arXiv:1906.11615
Sanabria, S.J., Goksel, O.: Hand-held sound-speed imaging based on ultrasound reflector delineation. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9900, pp. 568–576. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46720-7_66
Sanabria, S.J., Ozkan, E., Rominger, M., Goksel, O.: Spatial domain reconstruction for imaging speed-of-sound with pulse-echo ultrasound: simulation and in vivo study. Phys. Med. Biol. 63(21), 215015 (2018)
Sanabria, S., Rominger, M., Goksel, O.: Speed-of-sound imaging based on reflector delineation. IEEE Trans. Biomed. Eng. 66(7), 1949–1962 (2019)
Schwab, J., Antholzer, S., Haltmeier, M.: Learned backprojection for sparse and limited view photoacoustic tomography. In: Proceedings of SPIE Photons Plus Ultrasound: Imaging and Sensing, p. 1087837 (2019)
Siewerdsen, J., et al.: Multimode C-arm fluoroscopy, tomosynthesis, and cone-beam CT for image-guided interventions: from proof of principle to patient protocols. In: Proceedings of SPIE Medical Imaging, p. 65101A (2007)
Soler, L., et al.: 3D image reconstruction for comparison of algorithm database: a patient specific anatomical and medical image database. Technical report. IRCAD, Strasbourg, France (2010)
Vishnevskiy, V., Sanabria, S.J., Goksel, O.: Image reconstruction via variational network for real-time hand-held sound-speed imaging. In: Knoll, F., Maier, A., Rueckert, D. (eds.) MLMIR 2018. LNCS, vol. 11074, pp. 120–128. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00129-2_14
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P., et al.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
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)
Zheng, X., Ravishankar, S., Long, Y., Fessler, J.A.: PWLS-ULTRA: an efficient clustering and learning-based approach for low-dose 3D CT image reconstruction. IEEE Trans. Med. Imaging 37(6), 1498–1510 (2018)
Funding
It was provided by the Swiss National Science Foundation (SNSF).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Vishnevskiy, V., Rau, R., Goksel, O. (2019). Deep Variational Networks with Exponential Weighting for Learning Computed Tomography. In: Shen, D., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2019. MICCAI 2019. Lecture Notes in Computer Science(), vol 11769. Springer, Cham. https://doi.org/10.1007/978-3-030-32226-7_35
Download citation
DOI: https://doi.org/10.1007/978-3-030-32226-7_35
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32225-0
Online ISBN: 978-3-030-32226-7
eBook Packages: Computer ScienceComputer Science (R0)
