基于二维傅里叶Helgason-Ludwig一致性条件的截断CT数据改进外推方案。

IF 3.3 Q2 ENGINEERING, BIOMEDICAL International Journal of Biomedical Imaging Pub Date : 2017-01-01 Epub Date: 2017-07-20 DOI:10.1155/2017/1867025
Yan Xia, Martin Berger, Sebastian Bauer, Shiyang Hu, Andre Aichert, Andreas Maier
{"title":"基于二维傅里叶Helgason-Ludwig一致性条件的截断CT数据改进外推方案。","authors":"Yan Xia,&nbsp;Martin Berger,&nbsp;Sebastian Bauer,&nbsp;Shiyang Hu,&nbsp;Andre Aichert,&nbsp;Andreas Maier","doi":"10.1155/2017/1867025","DOIUrl":null,"url":null,"abstract":"<p><p>We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform (FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the parameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be used to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data. Results show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method.</p>","PeriodicalId":47063,"journal":{"name":"International Journal of Biomedical Imaging","volume":null,"pages":null},"PeriodicalIF":3.3000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2017/1867025","citationCount":"12","resultStr":"{\"title\":\"An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions.\",\"authors\":\"Yan Xia,&nbsp;Martin Berger,&nbsp;Sebastian Bauer,&nbsp;Shiyang Hu,&nbsp;Andre Aichert,&nbsp;Andreas Maier\",\"doi\":\"10.1155/2017/1867025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform (FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the parameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be used to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data. Results show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method.</p>\",\"PeriodicalId\":47063,\"journal\":{\"name\":\"International Journal of Biomedical Imaging\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.3000,\"publicationDate\":\"2017-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/2017/1867025\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Biomedical Imaging\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2017/1867025\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2017/7/20 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, BIOMEDICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Biomedical Imaging","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2017/1867025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2017/7/20 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"ENGINEERING, BIOMEDICAL","Score":null,"Total":0}
引用次数: 12

摘要

我们通过使用Helgason-Ludwig (HL)一致性条件来改进截断计算机断层扫描(CT)投影的数据外推,该条件在数学上描述了投影之间的信息重叠。首先,我们从理论上推导出HL一致性条件的二维傅里叶表示,从它们的原始公式(投影矩定理),为平行光束和扇形光束成像几何。推导结果表明,在二维傅里叶域中存在一个形成双楔形的零能区。这个观察结果在以前的文献中也被称为正弦图的傅里叶性质。这种表示的主要优点是可以通过二维快速傅里叶变换(FFT)有效地评估一致性条件。然后,我们提出了一种用均匀椭圆的数据外推截断投影的方法,其中参数是通过优化这些一致性条件来确定的。利用优化后椭圆的正投影完成数据的截断。该算法使用模拟数据和临床数据的重新投影进行评估。结果表明,与最先进的外推方法相比,该方法大大降低了均方根误差(RMSE)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

摘要图片

摘要图片

摘要图片

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions.

We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform (FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the parameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be used to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data. Results show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
12.00
自引率
0.00%
发文量
11
审稿时长
20 weeks
期刊介绍: The International Journal of Biomedical Imaging is managed by a board of editors comprising internationally renowned active researchers. The journal is freely accessible online and also offered for purchase in print format. It employs a web-based review system to ensure swift turnaround times while maintaining high standards. In addition to regular issues, special issues are organized by guest editors. The subject areas covered include (but are not limited to): Digital radiography and tomosynthesis X-ray computed tomography (CT) Magnetic resonance imaging (MRI) Single photon emission computed tomography (SPECT) Positron emission tomography (PET) Ultrasound imaging Diffuse optical tomography, coherence, fluorescence, bioluminescence tomography, impedance tomography Neutron imaging for biomedical applications Magnetic and optical spectroscopy, and optical biopsy Optical, electron, scanning tunneling/atomic force microscopy Small animal imaging Functional, cellular, and molecular imaging Imaging assays for screening and molecular analysis Microarray image analysis and bioinformatics Emerging biomedical imaging techniques Imaging modality fusion Biomedical imaging instrumentation Biomedical image processing, pattern recognition, and analysis Biomedical image visualization, compression, transmission, and storage Imaging and modeling related to systems biology and systems biomedicine Applied mathematics, applied physics, and chemistry related to biomedical imaging Grid-enabling technology for biomedical imaging and informatics
期刊最新文献
Noninvasive Assessment of Cardiopulmonary Hemodynamics Using Cardiovascular Magnetic Resonance Pulmonary Transit Time. Comparison of 3D Gradient-Echo Versus 2D Sequences for Assessing Shoulder Joint Image Quality in MRI. The Blood-Brain Barrier in Both Humans and Rats: A Perspective From 3D Imaging. Presegmenter Cascaded Framework for Mammogram Mass Segmentation. An End-to-End CRSwNP Prediction with Multichannel ResNet on Computed Tomography.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1