High-order total variation regularization approach for axially symmetric object tomography from a single radiograph

Raymond H. Chan*, Haixia Liang, Suhua Wei, Mila Nikolova, Xue Cheng Tai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


In this paper, we consider tomographic reconstruction for axially symmetric objects from a single radiograph formed by fan-beam X-rays. All contemporary methods are based on the assumption that the density is piecewise constant or linear. From a practical viewpoint, this is quite a restrictive approximation. The method we propose is based on high-order total variation regularization. Its main advantage is to reduce the staircase effect while keeping sharp edges and enable the recovery of smoothly varying regions. The optimization problem is solved using the augmented Lagrangian method which has been recently applied in image processing. Furthermore, we use a one-dimensional (1D) technique for fan-beam X-rays to approximate 2D tomographic reconstruction for cone-beam X-rays. For the 2D problem, we treat the cone beam as fan beam located at parallel planes perpendicular to the symmetric axis. Then the density of the whole object is recovered layer by layer. Numerical results in 1D show that the proposed method has improved the preservation of edge location and the accuracy of the density level when compared with several other contemporary methods. The 2D numerical tests show that cylindrical symmetric objects can be recovered rather accurately by our high-order regularization model.

Original languageEnglish
Pages (from-to)55-77
Number of pages23
JournalInverse Problems and Imaging
Issue number1
Publication statusPublished - 2015


  • Abel inversion
  • Augmented Lagrangian method
  • High-order total variation
  • Radiograph
  • Tomography


Dive into the research topics of 'High-order total variation regularization approach for axially symmetric object tomography from a single radiograph'. Together they form a unique fingerprint.

Cite this