Abstract
Image reconstruction in sparse view CT is a challenging ill-posed inverse problem, which aims at reconstructing a high-quality image from few and noisy measurements. As a prominent tool in the recent development of CT reconstruction, deep neural network (DNN) is mostly used as a denoising post-process or a regularization sub-module in some optimization unrolling method. As the problem of CT reconstruction essentially is about how to convert discrete Fourier transform in polar coordinates to its counterpart in Cartesian coordinates, this paper proposed to directly learn an interpolation scheme, modeled by a multi-scale DNN, for predicting 2D Fourier coefficients in Cartesian coordinates from the available ones in polar coordinates. The experiments showed that, in comparison to existing DNN-based solutions, the proposed DNN-based Fourier interpolation method not only provided the state-of-the-art performance, but also is much more computationally efficient.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Adler, J., Öktem, O.: Learned primal-dual reconstruction. IEEE Trans. Med. Imaging 37(6), 1322–1332 (2018)
Buzug, T.M.: Computed tomography. In: Springer Handbook of Medical Technology, pp. 311–342. Springer, Berlin (2011)
Chen, H., et al.: LEARN: learned experts’ assessment-based reconstruction network for sparse-data CT. IEEE Trans. Med. Imaging 37(6), 1333–1347 (2018)
Chen, H., et al.: Low-dose CT with a residual encoder-decoder convolutional neural network. IEEE Trans. Med. Imaging 36(12), 2524–2535 (2017)
Ding, Q., Chen, G., Zhang, X., Huang, Q., Ji, H., Gao, H.: Low-dose CT with deep learning regularization via proximal forward–backward splitting. Phys. Med. Biol. 65(12), 125009 (2020)
Ding, Q., Nan, Y., Gao, H., Ji, H.: Deep learning with adaptive hyper-parameters for low-dose CT image reconstruction. IEEE Trans. Comput. Imaging, 1–1 (2021). https://doi.org/10.1109/TCI.2021.3093003
Dong, B., Shen, Z., et al.: MRA based wavelet frames and applications. IAS Lecture Notes Series, Summer Program on “The Mathematics of Image Processing”, Park City Mathematics Institute. 19 (2010)
Gupta, H., Jin, K.H., Nguyen, H.Q., McCann, M.T., Unser, M.: CNN-based projected gradient descent for consistent CT image reconstruction. IEEE Trans. Med. Imaging 37(6), 1440–1453 (2018)
Hara, A.K., Paden, R.G., Silva, A.C., Kujak, J.L., Lawder, H.J., Pavlicek, W.: Iterative reconstruction technique for reducing body radiation dose at CT: feasibility study. Am. J. Roentgenol. 193(3), 764–771 (2009)
He, J., et al.: Optimizing a parameterized plug-and-play ADMM for iterative low-dose CT reconstruction. IEEE Trans. Med. Imaging 38(2), 371–382 (2018)
Jia, X., Dong, B., Lou, Y., Jiang, S.B.: GPU-based iterative cone-beam CT reconstruction using tight frame regularization. Phys. Med. Biol. 56(13), 3787 (2011)
Jin, K.H., McCann, M.T., Froustey, E., Unser, M.: Deep convolutional neural network for inverse problems in imaging. IEEE Trans. Med. Imaging 26(9), 4509–4522 (2017)
Katsura, M., et al.: Model-based iterative reconstruction technique for radiation dose reduction in chest CT: comparison with the adaptive statistical iterative reconstruction technique. Eur. Radiol. 22(8), 1613–1623 (2012)
Radon, J.: 1.1 Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Ber. Verh. Sächs. Akad. Wiss., Math. -Nat. KI. 69, 262–277 (1917)
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)
Silva, A.C., Lawder, H.J., Hara, A., Kujak, J., Pavlicek, W.: Innovations in CT dose reduction strategy: application of the adaptive statistical iterative reconstruction algorithm. Am. J. Roentgenol. 194(1), 191–199 (2010)
Sun, J., Li, H., Xu, Z., et al.: Deep ADMM-Net for compressive sensing MRI. In: Advances in Neural Information Processing Systems, pp. 10–18 (2016)
Wang, G.: A perspective on deep imaging. IEEE Access 4, 8914–8924 (2016)
Xu, Q., Yu, H., Mou, X., Zhang, L., Hsieh, J., Wang, G.: Low-dose X-ray CT reconstruction via dictionary learning. IEEE Trans. Med. Imaging 31(9), 1682–1697 (2012)
Ye, J.C., Han, Y., Cha, E.: Deep convolutional framelets: a general deep learning framework for inverse problems. SIAM J. Imaging Sci. 11(2), 991–1048 (2018)
Zeng, G.L.: Medical Image Reconstruction: A Conceptual Tutorial. Springer, New York (2010)
Zhang, X.-Q., Froment, J.: Constrained total variation minimization and application in computerized tomography. In: Rangarajan, A., Vemuri, B., Yuille, A.L. (eds.) EMMCVPR 2005. LNCS, vol. 3757, pp. 456–472. Springer, Heidelberg (2005). https://doi.org/10.1007/11585978_30
Zhang, X., Froment, J.: Total variation based fourier reconstruction and regularization for computer tomography. In: IEEE Nuclear Science Symposium Conference Record, 2005, vol. 4, pp. 2332–2336. IEEE (2005)
Acknowledgment
This work was supported by NSFC (No.11771288, No.12090024), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102) and Singapore MOE Academic Research Fund (MOE2017-T2-2-156, R-146-000-315-114).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Ding, Q., Ji, H., Gao, H., Zhang, X. (2021). Learnable Multi-scale Fourier Interpolation for Sparse View CT Image Reconstruction. In: de Bruijne, M., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2021. MICCAI 2021. Lecture Notes in Computer Science(), vol 12906. Springer, Cham. https://doi.org/10.1007/978-3-030-87231-1_28
Download citation
DOI: https://doi.org/10.1007/978-3-030-87231-1_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-87230-4
Online ISBN: 978-3-030-87231-1
eBook Packages: Computer ScienceComputer Science (R0)
