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Volume 34, Issue 6
Limited Tomography Reconstruction via Tight Frame and Simultaneous Sinogram Extrapolation

Jae Kyu Choi, Bin Dong & Xiaoqun Zhang

DOI: 10.4208/jcm.1605-m2016-0535

J. Comp. Math., 34 (2016), pp. 575-589.

Published online: 2016-12

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  • Abstract

X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered back-projection reconstruction method requires the complete knowledge of the projection data. In the case of limited data, the inverse problem of CT becomes more ill-posed, which makes the reconstructed image deteriorated by the artifacts. In this paper, we consider two dimensional CT reconstruction using the projections truncated along the spatial direction in the Radon domain. Over the decades, the numerous results including the sparsity model based approach has enabled the reconstruction of the image inside the region of interest (ROI) from the limited knowledge of the data. However, unlike these existing methods, we try to reconstruct the entire CT image from the limited knowledge of the sinogram via the tight frame regularization and the simultaneous sinogram extrapolation. Our proposed model shows more promising numerical simulation results compared with the existing sparsity model based approach.

  • Keywords

X-ray computed tomography, Limited tomography, Wavelet frame, Data driven tight frame, Bregmanized operator splitting algorithm, Sinogram extrapolation.

  • AMS Subject Headings

65N20, 65N21, 94A08.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jaycjk@sjtu.edu.cn (Jae Kyu Choi)

dongbin@math.pku.edu.cn (Bin Dong)

xqzhang@sjtu.edu.cn (Xiaoqun Zhang)

  • BibTex
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  • TXT
@Article{JCM-34-575, author = {Choi , Jae KyuDong , Bin and Zhang , Xiaoqun}, title = {Limited Tomography Reconstruction via Tight Frame and Simultaneous Sinogram Extrapolation}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {6}, pages = {575--589}, abstract = {

X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered back-projection reconstruction method requires the complete knowledge of the projection data. In the case of limited data, the inverse problem of CT becomes more ill-posed, which makes the reconstructed image deteriorated by the artifacts. In this paper, we consider two dimensional CT reconstruction using the projections truncated along the spatial direction in the Radon domain. Over the decades, the numerous results including the sparsity model based approach has enabled the reconstruction of the image inside the region of interest (ROI) from the limited knowledge of the data. However, unlike these existing methods, we try to reconstruct the entire CT image from the limited knowledge of the sinogram via the tight frame regularization and the simultaneous sinogram extrapolation. Our proposed model shows more promising numerical simulation results compared with the existing sparsity model based approach.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1605-m2016-0535}, url = {http://global-sci.org/intro/article_detail/jcm/9814.html} }
TY - JOUR T1 - Limited Tomography Reconstruction via Tight Frame and Simultaneous Sinogram Extrapolation AU - Choi , Jae Kyu AU - Dong , Bin AU - Zhang , Xiaoqun JO - Journal of Computational Mathematics VL - 6 SP - 575 EP - 589 PY - 2016 DA - 2016/12 SN - 34 DO - http://doi.org/10.4208/jcm.1605-m2016-0535 UR - https://global-sci.org/intro/article_detail/jcm/9814.html KW - X-ray computed tomography, Limited tomography, Wavelet frame, Data driven tight frame, Bregmanized operator splitting algorithm, Sinogram extrapolation. AB -

X-ray computed tomography (CT) is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered back-projection reconstruction method requires the complete knowledge of the projection data. In the case of limited data, the inverse problem of CT becomes more ill-posed, which makes the reconstructed image deteriorated by the artifacts. In this paper, we consider two dimensional CT reconstruction using the projections truncated along the spatial direction in the Radon domain. Over the decades, the numerous results including the sparsity model based approach has enabled the reconstruction of the image inside the region of interest (ROI) from the limited knowledge of the data. However, unlike these existing methods, we try to reconstruct the entire CT image from the limited knowledge of the sinogram via the tight frame regularization and the simultaneous sinogram extrapolation. Our proposed model shows more promising numerical simulation results compared with the existing sparsity model based approach.

Choi , Jae KyuDong , Bin and Zhang , Xiaoqun. (2016). Limited Tomography Reconstruction via Tight Frame and Simultaneous Sinogram Extrapolation. Journal of Computational Mathematics. 34 (6). 575-589. doi:10.4208/jcm.1605-m2016-0535
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