Volume 34, Issue 6
Robust Frame Based X-Ray CT Reconstruction

Jia Li, Chuang Miao, Zuowei Shen, Ge Wang & Hengyong Yu

J. Comp. Math., 34 (2016), pp. 683-704.

Published online: 2016-12

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  • Abstract

As X-ray computed tomography (CT) is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this purpose, one may use the TV based methods or wavelet frame based methods to reconstruct high quality images from reduced number of projections. Furthermore, by using the interior tomography scheme which only illuminates a region-of-interest (ROI), one can save more radiation dose. In this paper, a robust wavelet frame regularization based model is proposed for both global reconstruction and interior tomography. The model can help to reduce the errors caused by mismatch of the huge sparse projection matrix. A three-system decomposition scheme is applied to decompose the reconstructed images into three different parts: cartoon, artifacts and noise. Therefore, by discarding the estimated artifacts and noise parts, the reconstructed images can be obtained with less noise and artifacts. Similar to other frame based image restoration models, the model can be efficiently solved by the split Bregman algorithm. Numerical simulations show that the proposed model outperforms the FBP and SART+TV methods in terms of preservation of sharp edges, mean structural similarity (SSIM), contrast-to-noise ratio, relative error and correlations. For example, for real sheep lung reconstruction, the proposed method can reach the mean structural similarity as high as 0.75 using only 100 projections while the FBP and the SART+TV methods need more than 200 projections. Additionally, the proposed robust method is applicable for interior and exterior tomography with better performance compared to the FBP and the SART+TV methods.

  • Keywords

Computed tomography Wavelet frame Split Bregman algorithm

  • AMS Subject Headings

15A15 15A09 15A23.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lij25@rpi.edu (Jia Li)

cmiaowfu@gmail.com (Chuang Miao)

matzuows@nus.edu.sg (Zuowei Shen)

wangg6@rpi.edu (Ge Wang)

hengyong-yu@ieee.org (Hengyong Yu)

  • BibTex
  • RIS
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@Article{JCM-34-683, author = {Li , Jia and Miao , Chuang and Shen , Zuowei and Wang , Ge and Yu , Hengyong }, title = {Robust Frame Based X-Ray CT Reconstruction}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {6}, pages = {683--704}, abstract = { As X-ray computed tomography (CT) is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this purpose, one may use the TV based methods or wavelet frame based methods to reconstruct high quality images from reduced number of projections. Furthermore, by using the interior tomography scheme which only illuminates a region-of-interest (ROI), one can save more radiation dose. In this paper, a robust wavelet frame regularization based model is proposed for both global reconstruction and interior tomography. The model can help to reduce the errors caused by mismatch of the huge sparse projection matrix. A three-system decomposition scheme is applied to decompose the reconstructed images into three different parts: cartoon, artifacts and noise. Therefore, by discarding the estimated artifacts and noise parts, the reconstructed images can be obtained with less noise and artifacts. Similar to other frame based image restoration models, the model can be efficiently solved by the split Bregman algorithm. Numerical simulations show that the proposed model outperforms the FBP and SART+TV methods in terms of preservation of sharp edges, mean structural similarity (SSIM), contrast-to-noise ratio, relative error and correlations. For example, for real sheep lung reconstruction, the proposed method can reach the mean structural similarity as high as 0.75 using only 100 projections while the FBP and the SART+TV methods need more than 200 projections. Additionally, the proposed robust method is applicable for interior and exterior tomography with better performance compared to the FBP and the SART+TV methods.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1608-m2016-0499}, url = {http://global-sci.org/intro/article_detail/jcm/9820.html} }
TY - JOUR T1 - Robust Frame Based X-Ray CT Reconstruction AU - Li , Jia AU - Miao , Chuang AU - Shen , Zuowei AU - Wang , Ge AU - Yu , Hengyong JO - Journal of Computational Mathematics VL - 6 SP - 683 EP - 704 PY - 2016 DA - 2016/12 SN - 34 DO - http://doi.org/10.4208/jcm.1608-m2016-0499 UR - https://global-sci.org/intro/article_detail/jcm/9820.html KW - Computed tomography KW - Wavelet frame KW - Split Bregman algorithm AB - As X-ray computed tomography (CT) is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this purpose, one may use the TV based methods or wavelet frame based methods to reconstruct high quality images from reduced number of projections. Furthermore, by using the interior tomography scheme which only illuminates a region-of-interest (ROI), one can save more radiation dose. In this paper, a robust wavelet frame regularization based model is proposed for both global reconstruction and interior tomography. The model can help to reduce the errors caused by mismatch of the huge sparse projection matrix. A three-system decomposition scheme is applied to decompose the reconstructed images into three different parts: cartoon, artifacts and noise. Therefore, by discarding the estimated artifacts and noise parts, the reconstructed images can be obtained with less noise and artifacts. Similar to other frame based image restoration models, the model can be efficiently solved by the split Bregman algorithm. Numerical simulations show that the proposed model outperforms the FBP and SART+TV methods in terms of preservation of sharp edges, mean structural similarity (SSIM), contrast-to-noise ratio, relative error and correlations. For example, for real sheep lung reconstruction, the proposed method can reach the mean structural similarity as high as 0.75 using only 100 projections while the FBP and the SART+TV methods need more than 200 projections. Additionally, the proposed robust method is applicable for interior and exterior tomography with better performance compared to the FBP and the SART+TV methods.
Jia Li , Chuang Miao , Zuowei Shen, Ge Wang & Hengyong Yu . (2020). Robust Frame Based X-Ray CT Reconstruction. Journal of Computational Mathematics. 34 (6). 683-704. doi:10.4208/jcm.1608-m2016-0499
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