A Tomographic Reconstruction Method using Coordinate-based Neural Network with Spatial Regularization

Keywords: Tomographic Reconstruction, Coordinate-based Neural Network, Inverse Problem

Abstract

Tomographic reconstruction is concerned with computing the cross-sections of an object from a finite number of projections. Many conventional methods represent the cross-sections as images on a regular grid. In this paper, we study a recent coordinate-based neural network for tomographic reconstruction, where the network inputs a spatial coordinate and outputs the attenuation coefficient on the coordinate. This coordinate-based network allows the continuous representation of an object. Based on this network, we propose a spatial regularization term, to obtain a high-quality reconstruction. Experimental results on synthetic data show that the regularization term improves the reconstruction quality significantly, compared to the baseline. We also provide an ablation study for different architecture configurations and hyper-parameters.

References

J. Adler and O. ¨Oktem. Solving ill-posed inverse problems using iterative deep neural networks. Inverse Problems, 33(12), 2017. https://doi.org/10.1088/1361-6420/aa9581

J. Adler and O. ¨Oktem. Learned Primal-dual Reconstruction. IEEE Trans. Med. Imaging, 37(6), 2018. https://doi.org/10.1109/TMI.2018.2799231

A. H. Andersen and A. C. Kak. Simultaneous Algebraic Reconstruction Technique (SART): A superior implementation of the ART algorithm. Ultrason. Imaging, 6(1), 1984. https://doi.org/10.1177/016173468400600107

T. Brox, A. Bruhn, N. Papenberg, and J. Weickert. High accuracy optical flow estimation based on a theory for warping. In European Conference on Computer Vision (ECCV), 2004. https://doi.org/10.1007/978-3-540-24673-2_3

T. M. Buzug. Computed Tomography from Photon Statistics to Modern Cone Beam CT. Springer, 2008.

S. B. Coban and S. A. McDonald. SophiaBeads dataset project, Mar. 2015.

M. Gadelha, R. Wang, and S. Maji. Shape Reconstruction Using Differentiable Projections and Deep Priors. In International Conference on Computer Vision (ICCV), 2019. https://doi.org/10.1109/ICCV.2019.00011

J. He, Y. Wang, and J. Ma. Radon inversion via deep learning. IEEE Transactions on Medical Imaging, 39(6):2076-2087, 2020. https://doi.org/10.1109/TMI.2020.2964266

M. Innes. Flux: Elegant machine learning with julia. J. Open Source Softw., 2018. https://doi.org/10.21105/joss.00602

K. H. Jin, M. T. McCann, E. Froustey, and M. Unser. Deep Convolutional Neural Network for Inverse Problems in Imaging. IEEE Trans. Image Process., 26(9), 2017. https://doi.org/10.1109/TIP.2017.2713099

D. Kingma and J. Ba. Adam: A method for stochastic optimization. In International Conference on Learning Representations, 2015.

B. Mildenhall, P. P. Srinivasan, M. Tancik, J. T. Barron, R. Ramamoorthi, and R. Ng. NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis. In European Conference on Computer Vision (ECCV), 2020. https://doi.org/10.1007/978-3-030-58452-8_24

L. I. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms. Phys. Nonlinear Phenom., 60(1-4), 1992. https://doi.org/10.1016/0167-2789(92)90242-F

E. Y. Sidky, J. H. Jørgensen, and X. Pan. Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm. Phys. Med. Biol., 57(10), 2012. https://doi.org/10.1088/0031-9155/57/10/3065

V. Sitzmann, J. N. P. Martel, A. W. Bergman, D. B. Lindell, and G. Wetzstein. Implicit Neural Representations with Periodic Activation Functions. arXiv:2006.09661, 2020.

M. Tancik, P. P. Srinivasan, B. Mildenhall, S. Fridovich-Keil, N. Raghavan, U. Singhal,R. Ramamoorthi, J. T. Barron, and R. Ng. Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains. arXiv:2006.10739, 2020.

D. Ulyanov, A. Vedaldi, and V. Lempitsky. Deep image prior. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2018.

T. Wurfl, M. Hoffmann, V. Christlein, K. Breininger, Y. Huang, M. Unberath, and A. K. Maier. Deep Learning Computed Tomography: Learning Projection-Domain Weights From Image Domain in Limited Angle Problems. IEEE Trans. Med. Imaging, 37(6), 2018. https://doi.org/10.1109/TMI.2018.2833499

B. Zhu, J. Z. Liu, S. F. Cauley, B. R. Rosen, and M. S. Rosen. Image reconstruction by domain-transform manifold learning. Nature, 555(7697), 2018. https://doi.org/10.1038/nature25988

Published
2021-04-19