John’s Equation-based Consistency Condition and Corrupted Projection Restoration in Circular Trajectory Cone Beam CT

Abstract In transmitted X-ray tomography imaging, the acquired projections may be corrupted for various reasons, such as defective detector cells and beam-stop array scatter correction problems. In this study, we derive a consistency condition for cone-beam projections and propose a method to restor...

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Autores principales:	Jianhui Ma, Shuyu Wu, Hongliang Qi, Bin Li, Hao Yan, Linghong Zhou, Yuan Xu
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/0ee44e712cef4c78834c29c9c899350d
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spelling	oai:doaj.org-article:0ee44e712cef4c78834c29c9c899350d2021-12-02T15:05:35ZJohn’s Equation-based Consistency Condition and Corrupted Projection Restoration in Circular Trajectory Cone Beam CT10.1038/s41598-017-05249-52045-2322https://doaj.org/article/0ee44e712cef4c78834c29c9c899350d2017-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-05249-5https://doaj.org/toc/2045-2322Abstract In transmitted X-ray tomography imaging, the acquired projections may be corrupted for various reasons, such as defective detector cells and beam-stop array scatter correction problems. In this study, we derive a consistency condition for cone-beam projections and propose a method to restore lost data in corrupted projections. In particular, the relationship of the geometry parameters in circular trajectory cone-beam computed tomography (CBCT) is utilized to convert an ultra-hyperbolic partial differential equation (PDE) into a second-order PDE. The second-order PDE is then transformed into a first-order ordinary differential equation in the frequency domain. The left side of the equation for the newly derived consistency condition is the projection derivative of the current and adjacent views, whereas the right side is the projection derivative of the geometry parameters. A projection restoration method is established based on the newly derived equation to restore corrupted data in projections in circular trajectory CBCT. The proposed method is tested in beam-stop array scatter correction, metal artifact reduction, and abnormal pixel correction cases to evaluate the performance of the consistency condition and corrupted projection restoration method. Qualitative and quantitative results demonstrate that the present method has considerable potential in restoring lost data in corrupted projections.Jianhui MaShuyu WuHongliang QiBin LiHao YanLinghong ZhouYuan XuNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-17 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Jianhui Ma Shuyu Wu Hongliang Qi Bin Li Hao Yan Linghong Zhou Yuan Xu John’s Equation-based Consistency Condition and Corrupted Projection Restoration in Circular Trajectory Cone Beam CT
description	Abstract In transmitted X-ray tomography imaging, the acquired projections may be corrupted for various reasons, such as defective detector cells and beam-stop array scatter correction problems. In this study, we derive a consistency condition for cone-beam projections and propose a method to restore lost data in corrupted projections. In particular, the relationship of the geometry parameters in circular trajectory cone-beam computed tomography (CBCT) is utilized to convert an ultra-hyperbolic partial differential equation (PDE) into a second-order PDE. The second-order PDE is then transformed into a first-order ordinary differential equation in the frequency domain. The left side of the equation for the newly derived consistency condition is the projection derivative of the current and adjacent views, whereas the right side is the projection derivative of the geometry parameters. A projection restoration method is established based on the newly derived equation to restore corrupted data in projections in circular trajectory CBCT. The proposed method is tested in beam-stop array scatter correction, metal artifact reduction, and abnormal pixel correction cases to evaluate the performance of the consistency condition and corrupted projection restoration method. Qualitative and quantitative results demonstrate that the present method has considerable potential in restoring lost data in corrupted projections.
format	article
author	Jianhui Ma Shuyu Wu Hongliang Qi Bin Li Hao Yan Linghong Zhou Yuan Xu
author_facet	Jianhui Ma Shuyu Wu Hongliang Qi Bin Li Hao Yan Linghong Zhou Yuan Xu
author_sort	Jianhui Ma
title	John’s Equation-based Consistency Condition and Corrupted Projection Restoration in Circular Trajectory Cone Beam CT
title_short	John’s Equation-based Consistency Condition and Corrupted Projection Restoration in Circular Trajectory Cone Beam CT
title_full	John’s Equation-based Consistency Condition and Corrupted Projection Restoration in Circular Trajectory Cone Beam CT
title_fullStr	John’s Equation-based Consistency Condition and Corrupted Projection Restoration in Circular Trajectory Cone Beam CT
title_full_unstemmed	John’s Equation-based Consistency Condition and Corrupted Projection Restoration in Circular Trajectory Cone Beam CT
title_sort	john’s equation-based consistency condition and corrupted projection restoration in circular trajectory cone beam ct
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/0ee44e712cef4c78834c29c9c899350d
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John’s Equation-based Consistency Condition and Corrupted Projection Restoration in Circular Trajectory Cone Beam CT

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