Inverse Fourier Transform in the Gamma Coordinate System

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dc.contributor.authorWei, Yuchuanen
dc.contributor.authorYu, Hengyongen
dc.contributor.authorWang, Geen
dc.contributor.departmentSchool of Biomedical Engineering and Sciencesen
dc.date.accessioned2017-09-18T09:54:32Zen
dc.date.available2017-09-18T09:54:32Zen
dc.date.issued2010-10-26en
dc.date.updated2017-09-18T09:54:32Zen
dc.description.abstractThis paper provides auxiliary results for our general scheme of computed tomography. In 3D parallel-beam geometry, we first demonstrate that the inverse Fourier transform in different coordinate systems leads to different reconstruction formulas and explain why the Radon formula cannot directly work with truncated projection data. Also, we introduce a gamma coordinate system, analyze its properties, compute the Jacobian of the coordinate transform, and define weight functions for the inverse Fourier transform assuming a simple scanning model. Then, we generate Orlov's theorem and a weighted Radon formula from the inverse Fourier transform in the new system. Furthermore, we present the motion equation of the frequency plane and the conditions for sharp points of the instantaneous rotation axis. Our analysis on the motion of the frequency plane is related to the Frenet-Serret theorem in the differential geometry.en
dc.description.versionPublished versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationYuchuan Wei, Hengyong Yu, and Ge Wang, “Inverse Fourier Transform in the Gamma Coordinate System,” International Journal of Biomedical Imaging, vol. 2011, Article ID 285130, 16 pages, 2011. doi:10.1155/2011/285130en
dc.identifier.doihttps://doi.org/10.1155/2011/285130en
dc.identifier.urihttp://hdl.handle.net/10919/79030en
dc.language.isoenen
dc.publisherHindawien
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.holderCopyright © 2011 Yuchuan Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.titleInverse Fourier Transform in the Gamma Coordinate Systemen
dc.title.serialInternational Journal of Biomedical Imagingen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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