Skip to main content
Top
Published in: Journal of Digital Imaging 1/2023

29-08-2022 | Computed Tomography | Original Paper

Interior Reconstruction from Truncated Projection Data in Cone-beam Computed Tomography

Authors: Wang Xianchao, Li Shaoyi, Hou Changhui

Published in: Journal of Imaging Informatics in Medicine | Issue 1/2023

Login to get access

Abstract

The interior reconstruction of completely truncated projection data is a frontier research hotspot in cone-beam computed tomography (CBCT) application. It is difficult to find a method with acceptable accuracy and high efficiency to solve it. Based on the simplified algebraic reconstruction technique (S-ART) algorithm and the filtered back projection (FBP) algorithm with the new filter, an efficient and feasible interior reconstruction algorithm is proposed in this paper. The algorithm uses the S-ART algorithm to quickly recover the complete projection data and then uses the new ramp filter which can suppress the high-frequency noise in the projection data to filter the recovered complete projection data. Finally, the interior reconstructed images are obtained by back projection. The computational complexity of the proposed algorithm is close to that of the FBP algorithm for the reconstruction of the whole object, and the reconstructed image quality is acceptable, which provides an effective method for interior reconstruction in CBCT. Simulation results show the effectiveness of the method.
Literature
1.
go back to reference S. J. Tang, B. L. Li, Z. W. Qiao, et al., An imperceptible incorrectness in deriving data consistency condition from John's equation for cone-beam CT imaging, Optik 202(3) (2020) 163603.CrossRef S. J. Tang, B. L. Li, Z. W. Qiao, et al., An imperceptible incorrectness in deriving data consistency condition from John's equation for cone-beam CT imaging, Optik 202(3) (2020) 163603.CrossRef
2.
go back to reference X. C. Wang, Z. Y. Tang, B. Yan, et al., Interior reconstruction method based on rotation-translation scanning model, Journal of X-ray Science and Technology 22(1) (2014) 37-45.CrossRefPubMed X. C. Wang, Z. Y. Tang, B. Yan, et al., Interior reconstruction method based on rotation-translation scanning model, Journal of X-ray Science and Technology 22(1) (2014) 37-45.CrossRefPubMed
3.
go back to reference X. C. Wang, G. E. Hu, Y. Bin, et al., Fast low-dose reconstruction from truncated data in dental CT, IEEE Transactions on Nuclear Science 60(1) (2013) 174-181.CrossRef X. C. Wang, G. E. Hu, Y. Bin, et al., Fast low-dose reconstruction from truncated data in dental CT, IEEE Transactions on Nuclear Science 60(1) (2013) 174-181.CrossRef
4.
go back to reference B. D. Smith, Image reconstruction from cone-beam projections: necessary and sufficient condition and reconstruction method, IEEE Transactions on Medical Imaging 4(1) (1985) 14-28.CrossRefPubMed B. D. Smith, Image reconstruction from cone-beam projections: necessary and sufficient condition and reconstruction method, IEEE Transactions on Medical Imaging 4(1) (1985) 14-28.CrossRefPubMed
5.
go back to reference G. Wang, H. Y. Yu, The meaning of interior tomography, Physics in Medicine and Biology 58(16) (2013) 161-186.CrossRef G. Wang, H. Y. Yu, The meaning of interior tomography, Physics in Medicine and Biology 58(16) (2013) 161-186.CrossRef
6.
go back to reference A. Faridani, E. L. Ritman, K. T. Smith, Local tomography, SIAM Journal on Applied Mathematics 52(2) (1992) 459-484.CrossRef A. Faridani, E. L. Ritman, K. T. Smith, Local tomography, SIAM Journal on Applied Mathematics 52(2) (1992) 459-484.CrossRef
7.
go back to reference A. J. Katsevich, A. G. Ramm, Pseudolocal tomography, SIAM Journal on Applied Mathematics 56(1) (1996) 167-191.CrossRef A. J. Katsevich, A. G. Ramm, Pseudolocal tomography, SIAM Journal on Applied Mathematics 56(1) (1996) 167-191.CrossRef
8.
go back to reference M. Bhatia, W. C. Karl, A. S. Willsky, A wavelet-based method for multiscale tomographic reconstruction, IEEE Transactions On Medical Imaging 15(1) (1996) 92-101.CrossRefPubMed M. Bhatia, W. C. Karl, A. S. Willsky, A wavelet-based method for multiscale tomographic reconstruction, IEEE Transactions On Medical Imaging 15(1) (1996) 92-101.CrossRefPubMed
9.
go back to reference F. R. Farrokhi, K. J. R. Liu, C. A. Berenstein, et al., Wavelet-based multiresolution local tomography, IEEE Transaction on Image Processing 10(6) (1997) 1412-1429.CrossRef F. R. Farrokhi, K. J. R. Liu, C. A. Berenstein, et al., Wavelet-based multiresolution local tomography, IEEE Transaction on Image Processing 10(6) (1997) 1412-1429.CrossRef
10.
go back to reference S. Y. Zhao, G. Wang, Feldkamp-type cone beam tomography in the wavelet framework, IEEE Transactions on Medical Imaging 19(9) (2000) 922-929.CrossRefPubMed S. Y. Zhao, G. Wang, Feldkamp-type cone beam tomography in the wavelet framework, IEEE Transactions on Medical Imaging 19(9) (2000) 922-929.CrossRefPubMed
11.
go back to reference Y. B. Ye, H. Y. Yu, Y. C. Wei, et al., A general local reconstruction approach based on a truncated Hilbert transform, International Journal of Biomedical Imaging 1(1) (2007) 1-8. Y. B. Ye, H. Y. Yu, Y. C. Wei, et al., A general local reconstruction approach based on a truncated Hilbert transform, International Journal of Biomedical Imaging 1(1) (2007) 1-8.
12.
go back to reference H. Kudo, M. Courdurier, F. Noo, et al., Tiny a priori knowledge solves the interior problem in computed tomography, Physics in Medicine and Biology 53(9) (2008) 2207-2231.CrossRefPubMed H. Kudo, M. Courdurier, F. Noo, et al., Tiny a priori knowledge solves the interior problem in computed tomography, Physics in Medicine and Biology 53(9) (2008) 2207-2231.CrossRefPubMed
13.
go back to reference G. V. Gompel, M. Defrise, K. J. Batenburg, Reconstruction of a uniform star object from interior x-ray data: uniqueness, stability and algorithm, Inverse Problem 25(6) (2009) 1-19. G. V. Gompel, M. Defrise, K. J. Batenburg, Reconstruction of a uniform star object from interior x-ray data: uniqueness, stability and algorithm, Inverse Problem 25(6) (2009) 1-19.
14.
go back to reference L. Li, K. J. Kang, Z. Q. Chen, et al., A general region-of-interest image reconstruction approach with truncated Hilbert transform, Journal of X-ray Science and Technology 17(2) (2009)135-152.CrossRefPubMed L. Li, K. J. Kang, Z. Q. Chen, et al., A general region-of-interest image reconstruction approach with truncated Hilbert transform, Journal of X-ray Science and Technology 17(2) (2009)135-152.CrossRefPubMed
15.
go back to reference Z. L. Hu, Y. W. Zhang, J. B. Liu, et al., A feature refinement approach for statistical interior CT reconstruction, Physics in Medicine and Biology 61(14) (2016) 5311-5334.CrossRefPubMed Z. L. Hu, Y. W. Zhang, J. B. Liu, et al., A feature refinement approach for statistical interior CT reconstruction, Physics in Medicine and Biology 61(14) (2016) 5311-5334.CrossRefPubMed
16.
go back to reference Z. Y. Qu, X. M. Yan, J. X. Pan, et al., Sparse view CT image reconstruction based on total variation and wavelet frame regularization, IEEE Access 8 (2020) 57400-57413.CrossRef Z. Y. Qu, X. M. Yan, J. X. Pan, et al., Sparse view CT image reconstruction based on total variation and wavelet frame regularization, IEEE Access 8 (2020) 57400-57413.CrossRef
17.
go back to reference A. L. Cai, L. Li, L. Y. Wang, et al., Optimization-based region-of-interest reconstruction for X-ray computed tomography based on total variation and data derivative, Physica Medica 48 (2018) 91-102.CrossRefPubMed A. L. Cai, L. Li, L. Y. Wang, et al., Optimization-based region-of-interest reconstruction for X-ray computed tomography based on total variation and data derivative, Physica Medica 48 (2018) 91-102.CrossRefPubMed
18.
19.
go back to reference R. Gordon, R. Bender, G. T. Herman, Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography, Journal of Theoretical Biology 29(3) (1970) 471-481.CrossRefPubMed R. Gordon, R. Bender, G. T. Herman, Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography, Journal of Theoretical Biology 29(3) (1970) 471-481.CrossRefPubMed
20.
go back to reference Y. S. Zhao, X. Zhao, P. Zhang, An extended algebraic reconstruction technique (E-ART) for dual spectral CT, IEEE Transactions on Medical Imaging 34(3) (2015) 761-768.CrossRefPubMed Y. S. Zhao, X. Zhao, P. Zhang, An extended algebraic reconstruction technique (E-ART) for dual spectral CT, IEEE Transactions on Medical Imaging 34(3) (2015) 761-768.CrossRefPubMed
21.
go back to reference X. C. Wang, S. Y. Li, C. S. Jiang, Fast system matrix calculation based on voxel projection in cone-beam CT, Optik 231(2) (2021) 166422.CrossRef X. C. Wang, S. Y. Li, C. S. Jiang, Fast system matrix calculation based on voxel projection in cone-beam CT, Optik 231(2) (2021) 166422.CrossRef
22.
go back to reference R. L. Siddon, Fast calculation of the exact radiological path for a three-dimensional CT array, Medical Physics 12(2) (1985) 252-255.CrossRefPubMed R. L. Siddon, Fast calculation of the exact radiological path for a three-dimensional CT array, Medical Physics 12(2) (1985) 252-255.CrossRefPubMed
24.
go back to reference X. C. Wang, L. Li, C. Q. Yu, et al., Fast reconstruction of flat region in a super-short scan based on MD-FBP algorithm, Journal of X-Ray Science and Technology 20(1) (2012) 69-77.CrossRefPubMed X. C. Wang, L. Li, C. Q. Yu, et al., Fast reconstruction of flat region in a super-short scan based on MD-FBP algorithm, Journal of X-Ray Science and Technology 20(1) (2012) 69-77.CrossRefPubMed
25.
go back to reference L. A. Feldkamp, L. C. Davis, J. W. Kress, Practical cone-beam algorithm, Journal of the Optical Society America 1(A) (1984) 612–619. L. A. Feldkamp, L. C. Davis, J. W. Kress, Practical cone-beam algorithm, Journal of the Optical Society America 1(A) (1984) 612–619.
26.
go back to reference X. Tao, H. Zhang, Y. B. Wang, et al., VVBP-tensor in the FBP algorithm: its properties and application in low-dose CT reconstruction, IEEE Transactions on Medical Imaging 39(3) (2019) 764-776.CrossRefPubMed X. Tao, H. Zhang, Y. B. Wang, et al., VVBP-tensor in the FBP algorithm: its properties and application in low-dose CT reconstruction, IEEE Transactions on Medical Imaging 39(3) (2019) 764-776.CrossRefPubMed
27.
go back to reference L. A. Shepp, B. F. Logan, The Fourier reconstruction of a head section, IEEE Transactions on Nuclear Science, 21(3) (1974) 21-43.CrossRef L. A. Shepp, B. F. Logan, The Fourier reconstruction of a head section, IEEE Transactions on Nuclear Science, 21(3) (1974) 21-43.CrossRef
28.
go back to reference Y. C. Wei, G. Wang, An intuitive discussion on the ideal ramp filter in computed tomography, Computers and Mathematics with Applications 49(5) (2005) 731-740.CrossRef Y. C. Wei, G. Wang, An intuitive discussion on the ideal ramp filter in computed tomography, Computers and Mathematics with Applications 49(5) (2005) 731-740.CrossRef
29.
go back to reference X. C. Wang, Z. Y. Tang, Z. B. Zhu, et al., Cone-beam reconstruction of flat specimens in a super-short scan, Insight 57(10) (2015) 571-575.CrossRef X. C. Wang, Z. Y. Tang, Z. B. Zhu, et al., Cone-beam reconstruction of flat specimens in a super-short scan, Insight 57(10) (2015) 571-575.CrossRef
Metadata
Title
Interior Reconstruction from Truncated Projection Data in Cone-beam Computed Tomography
Authors
Wang Xianchao
Li Shaoyi
Hou Changhui
Publication date
29-08-2022
Publisher
Springer International Publishing
Published in
Journal of Imaging Informatics in Medicine / Issue 1/2023
Print ISSN: 2948-2925
Electronic ISSN: 2948-2933
DOI
https://doi.org/10.1007/s10278-022-00695-8

Other articles of this Issue 1/2023

Journal of Digital Imaging 1/2023 Go to the issue