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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR 2018: 0.881
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1569-3945
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Volume 21, Issue 6

Issues

Limited-angle cone-beam computed tomography image reconstruction by total variation minimization and piecewise-constant modification

Li Zeng
  • ICT Research Center, Key Laboratory of Optoelectronic Technology and System of the Education Ministry of China, Chongqing University, Chongqing, 400044; and College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P. R. China
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/ Jiqiang Guo
  • ICT Research Center, Key Laboratory of Optoelectronic Technology and System of the Education Ministry of China, Chongqing University, Chongqing, 400044; and College of Optoelectronic Engineering, Chongqing University, Chongqing, 400044, P. R. China
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/ Baodong Liu
Published Online: 2012-12-04 | DOI: https://doi.org/10.1515/jip-2011-0010

Abstract.

Because of x-ray dose considerations or practical mechanical restrictions, it may be interesting for some applications to perform limited-angle scanning. So the limited-angle problem is of practical significance in computed tomography (CT). Furthermore, it is an ill-posed problem. Total variation minimization (TVM) and projection on convex sets (POCS) based iterative reconstruction algorithm is comparatively valid for this undersampling CT reconstruction problem and can obtain comparatively good performance. But the reconstruction images have artifacts with gradual change gray nearby edges. In this paper, a simple but efficient method to eliminate such artifacts during the reconstruction is proposed. Based on the same assumption of the TVM algorithm, for the object whose density distribution is approximate piecewise-constant, we develop and investigate an improved iterative reconstruction algorithm for volume image reconstruction from limited-angle cone-beam scan, which is referred to as piecewise-constant modification TVM-POCS (PM-TVM-POCS) algorithm. The grays of voxels with gradually changed gray artifacts are modified in the TVM-POCS iteration process by the piecewise-constant modification algorithm which is regarded as a “collapse” process, and gradually approaches the true piecewise-constant image. The results of simulation experiments show that the presented modification algorithm can improve the quality of the reconstructed image obviously and it is steady to noise. This modification algorithm can also be applied to other reconstruction problems which have artifacts with gradual change gray.

Keywords: Cone-beam computed tomography; limited-angle; ill-posed problem; total variation minimization; piecewise-constant modification

About the article

Received: 2011-05-30

Published Online: 2012-12-04

Published in Print: 2013-12-01


Citation Information: Journal of Inverse and Ill-Posed Problems, Volume 21, Issue 6, Pages 735–754, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jip-2011-0010.

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