NDLI: Convergence and stability analysis of the half thresholding based few-view CT reconstruction

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Convergence and stability analysis of the half thresholding based few-view CT reconstruction

Content Provider	Scilit
Author	Huang, Hua Lu, Chengwu Zhang, Lingli Wang, Weiwei
Copyright Year	2020
Abstract	The projection data obtained using the computed tomography (CT) technique are often incomplete and inconsistent owing to the radiation exposure and practical environment of the CT process, which may lead to a few-view reconstruction problem. Reconstructing an object from few projection views is often an ill-posed inverse problem. To solve such problems, regularization is an effective technique, in which the ill-posed problem is approximated considering a family of neighboring well-posed problems. In this study, we considered the $ℓ_{1 / 2}$ regularization to solve such ill-posed problems. Subsequently, the half thresholding algorithm was employed to solve the $ℓ_{1 / 2}$ regularization-based problem. The convergence analysis of the proposed method was performed, and the error bound between the reference image and reconstructed image was clarified. Finally, the stability of the proposed method was analyzed. The result of numerical experiments demonstrated that the proposed method can outperform the classical reconstruction algorithms in terms of noise suppression and preserving the details of the reconstructed image.
Related Links	https://www.degruyter.com/downloadpdf/journals/jiip/ahead-of-print/article-10.1515-jiip-2020-0003/article-10.1515-jiip-2020-0003.pdf
Ending Page	847
Page Count	19
Starting Page	829
ISSN	09280219
e-ISSN	15693945
DOI	10.1515/jiip-2020-0003
Journal	Journal of Inverse and Ill-Posed Problems
Issue Number	6
Volume Number	28
Language	English
Publisher	Walter de Gruyter GmbH
Publisher Date	2020-12-01
Access Restriction	Open
Subject Keyword	Journal of Inverse and Ill-posed Problems Applied Mathematics Inverse Problems Computed Tomography Image Reconstruction Wavelet Frames Half Thresholding 15a29 90c90 44a12 94a08 Journal: Journal of Inverse and Ill-Posed Problems, Vol- 28, Issue- 1
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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