CT image reconstruction by spatial-Radon domain data-driven tight frame regularization

Ruohan Zhan, Bin Dong

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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 languageEnglish (US)
Pages (from-to)1063-1083
Number of pages21
JournalSIAM Journal on Imaging Sciences
Issue number3
StatePublished - Jul 26 2016


  • Computed tomography
  • Data-driven tight frames
  • Sparse approximation
  • Spatial-Radon domain reconstruction

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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