Abstract
This paper proposes a spatial-Radon domain computed tomography (CT) image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of the joint image and Radon domain inpainting model of Dong, Li, and Shen [J. Sci. Com-put., 54 (2013), pp. 333-349] and that of the data-driven tight frames for image denoising [J.-F. Cai, H. Ji, Z. Shen, and G.-B. Ye, Appl. Comput. Harmon. Anal., 37 (2014), p. 89-105]. It is different from existing models in that both the CT image and its corresponding high quality projection image are reconstructed simultaneously using sparsity priors by tight frames that are adaptively learned from the data to provide optimal sparse approximations. An alternative minimization algorithm is designed to solve the proposed model, which is nonsmooth and nonconvex. Convergence analysis of the algorithm is provided. Numerical experiments show that the SRD-DDTF model is superior to the model of Dong, Li, and Shen [J. Sci. Comput., 54 (2013), pp. 333-349] especially in recovering some subtle structures in the images.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1063-1083 |
| Number of pages | 21 |
| Journal | SIAM Journal on Imaging Sciences |
| Volume | 9 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jul 26 2016 |
| Externally published | Yes |
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Keywords
- Computed tomography
- Data-driven tight frames
- Sparse approximation
- Spatial-Radon domain reconstruction
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
CT image reconstruction by spatial-Radon domain data-driven tight frame regularization. / Zhan, Ruohan; Dong, Bin.
In: SIAM Journal on Imaging Sciences, Vol. 9, No. 3, 26.07.2016, p. 1063-1083.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - CT image reconstruction by spatial-Radon domain data-driven tight frame regularization
AU - Zhan, Ruohan
AU - Dong, Bin
PY - 2016/7/26
Y1 - 2016/7/26
N2 - This paper proposes a spatial-Radon domain computed tomography (CT) image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of the joint image and Radon domain inpainting model of Dong, Li, and Shen [J. Sci. Com-put., 54 (2013), pp. 333-349] and that of the data-driven tight frames for image denoising [J.-F. Cai, H. Ji, Z. Shen, and G.-B. Ye, Appl. Comput. Harmon. Anal., 37 (2014), p. 89-105]. It is different from existing models in that both the CT image and its corresponding high quality projection image are reconstructed simultaneously using sparsity priors by tight frames that are adaptively learned from the data to provide optimal sparse approximations. An alternative minimization algorithm is designed to solve the proposed model, which is nonsmooth and nonconvex. Convergence analysis of the algorithm is provided. Numerical experiments show that the SRD-DDTF model is superior to the model of Dong, Li, and Shen [J. Sci. Comput., 54 (2013), pp. 333-349] especially in recovering some subtle structures in the images.
AB - This paper proposes a spatial-Radon domain computed tomography (CT) image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of the joint image and Radon domain inpainting model of Dong, Li, and Shen [J. Sci. Com-put., 54 (2013), pp. 333-349] and that of the data-driven tight frames for image denoising [J.-F. Cai, H. Ji, Z. Shen, and G.-B. Ye, Appl. Comput. Harmon. Anal., 37 (2014), p. 89-105]. It is different from existing models in that both the CT image and its corresponding high quality projection image are reconstructed simultaneously using sparsity priors by tight frames that are adaptively learned from the data to provide optimal sparse approximations. An alternative minimization algorithm is designed to solve the proposed model, which is nonsmooth and nonconvex. Convergence analysis of the algorithm is provided. Numerical experiments show that the SRD-DDTF model is superior to the model of Dong, Li, and Shen [J. Sci. Comput., 54 (2013), pp. 333-349] especially in recovering some subtle structures in the images.
KW - Computed tomography
KW - Data-driven tight frames
KW - Sparse approximation
KW - Spatial-Radon domain reconstruction
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UR - http://www.scopus.com/inward/citedby.url?scp=84989298930&partnerID=8YFLogxK
U2 - 10.1137/16M105928X
DO - 10.1137/16M105928X
M3 - Article
AN - SCOPUS:84989298930
VL - 9
SP - 1063
EP - 1083
JO - SIAM Journal on Imaging Sciences
JF - SIAM Journal on Imaging Sciences
SN - 1936-4954
IS - 3
ER -