Published by De Gruyter May 9, 2018

A non-smooth and non-convex regularization method for limited-angle CT image reconstruction

Lingli Zhang , Li Zeng , Chengxiang Wang and Yumeng Guo

From the journal Journal of Inverse and Ill-posed Problems

https://doi.org/10.1515/jiip-2017-0042

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Abstract

Restricted by the practical applications and radiation exposure of computed tomography (CT), the obtained projection data is usually incomplete, which may lead to a limited-angle reconstruction problem. Whereas reconstructing an object from limited-angle projection views is a challenging and ill-posed inverse problem. Fortunately, the regularization methods offer an effective way to deal with that. Recently, several researchers are absorbed in ℓ1 regularization to address such problem, but it has some problems for suppressing the limited-angle slope artifacts around edges due to incomplete projection data. In this paper, in order to surmount the ill-posedness, a non-smooth and non-convex method that is based on ℓ0 and ℓ1 regularization is presented to better deal with the limited-angle problem. Firstly, the splitting technique is utilized to deal with the presented approach called LWPC-ST-IHT. Afterwards, some propositions and convergence analysis of the presented approach are established. Numerical implementations show that our approach is more capable of suppressing the slope artifacts compared with the classical and state of the art iterative reconstruction algorithms.

Keywords: Inverse problems; computed tomography; image reconstruction; limited-angle; regularization; wavelet tight frames

MSC 2010: 15A29; 90C90; 44A12; 94A08

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 61271313

Award Identifier / Grant number: 61471070

Funding statement: This work is supported by the National Natural Science Foundation of China (Grants 61271313, 61471070) and National Instrumentation Program of China (2013YQ030629).

Acknowledgements

We thank the engineering research center of industrial computed tomography nondestructive testing of Chongqing university for providing us with the actual gear data. Furthermore, we thank the reviewers for the valuable comments and suggestions.

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Received: 2017-04-25

Revised: 2018-01-09

Accepted: 2018-03-13

Published Online: 2018-05-09

Published in Print: 2018-12-01

A non-smooth and non-convex regularization method for limited-angle CT image reconstruction

Abstract

Acknowledgements

References

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