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Article

CT Image Reconstruction via Nonlocal Low-Rank Regularization and Data-Driven Tight Frame

1
School of Mathematics and Big Data, Dezhou University, Dezhou 253023, China
2
Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, China
3
Financial Department of Dezhou University, Dezhou 253023, China
*
Author to whom correspondence should be addressed.
Academic Editor: Nikolai A. Sidorov
Symmetry 2021, 13(10), 1873; https://doi.org/10.3390/sym13101873
Received: 29 August 2021 / Revised: 26 September 2021 / Accepted: 28 September 2021 / Published: 4 October 2021
X-ray computed tomography (CT) is widely used in medical applications, where many efforts have been made for decades to eliminate artifacts caused by incomplete projection. In this paper, we propose a new CT image reconstruction model based on nonlocal low-rank regularity and data-driven tight frame (NLR-DDTF). Unlike the Spatial-Radon domain data-driven tight frame regularization, the proposed NLR-DDTF model uses an asymmetric treatment for image reconstruction and Radon domain inpainting, which combines the nonlocal low-rank approximation method for spatial domain CT image reconstruction and data-driven tight frame-based regularization for Radon domain image inpainting. An alternative direction minimization algorithm is designed to solve the proposed model. Several numerical experiments and comparisons are provided to illustrate the superior performance of the NLR-DDTF method. View Full-Text
Keywords: Radon transform; image inpainting; nonlocal low-rank regularity; data-driven tight frame Radon transform; image inpainting; nonlocal low-rank regularity; data-driven tight frame
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MDPI and ACS Style

Shen, Y.; Sun, S.; Xu, F.; Liu, Y.; Yin, X.; Zhou, X. CT Image Reconstruction via Nonlocal Low-Rank Regularization and Data-Driven Tight Frame. Symmetry 2021, 13, 1873. https://doi.org/10.3390/sym13101873

AMA Style

Shen Y, Sun S, Xu F, Liu Y, Yin X, Zhou X. CT Image Reconstruction via Nonlocal Low-Rank Regularization and Data-Driven Tight Frame. Symmetry. 2021; 13(10):1873. https://doi.org/10.3390/sym13101873

Chicago/Turabian Style

Shen, Yanfeng, Shuli Sun, Fengsheng Xu, Yanqin Liu, Xiuling Yin, and Xiaoshuang Zhou. 2021. "CT Image Reconstruction via Nonlocal Low-Rank Regularization and Data-Driven Tight Frame" Symmetry 13, no. 10: 1873. https://doi.org/10.3390/sym13101873

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