Gel'fand-Graev's Reconstruction Formula in the 3D Real Space - a Framework towards a General Interior Tomography Theory

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dc.contributorVirginia Tech-Wake Forest University School of Biomedical Engineering and Sciencesen
dc.contributor.authorYe, Yangboen
dc.contributor.authorYu, Hengyongen
dc.contributor.authorWang, Geen
dc.contributor.departmentSchool of Biomedical Engineering and Sciencesen
dc.date.accessed2014-11-26en
dc.date.accessioned2015-10-06T15:29:56Zen
dc.date.available2015-10-06T15:29:56Zen
dc.date.issued2010-05-31en
dc.description.abstractIn [1-4], I. M. Gel'fand and M. I. Graev proposed inversion formulas for x-ray transforms in different spaces. In particular, Gel’fand-Graev’s inversion formula [1] is a fundamental relationship linking projection data to the Hilbert transform of an image to be reconstructed. This finding was re-discovered in the CT field; see [5-9]. It has wide applications, including local reconstruction [10-11], backprojection filtration (BPF) [12], interior tomography [13-17], and limited-angle tomography [18]. For a survey, see [19, 20]. Despite its high information density, Gel’fand-Graev’s inversion formula [1] was cast in high dimensions and specialized terms, and difficult to follow for a well-trained engineer. In this poster, we represent this formula and its proof for the 1D x-ray transform in a 3D real space for easy access and further extension.en
dc.description.sponsorshipNational Institute of Biomedical Imaging and Bioengineering (U.S.) - Grant EB011785en
dc.description.sponsorshipNational Science Foundation (U.S.). Division of Civil, Mechanical and Manufacturing Innovation - Grant 0923297en
dc.format.mimetypeapplication/pdfen
dc.identifier.citationYe, Y., Yu, H., & Wang, G. (2010). Gel'fand-Graev's Reconstruction Formula in the 3d Real Space - a Framework Towards a General Interior Tomography Theory. Poster. Retrieved from http://www.imaging.sbes.vt.edu/posters/Poster-Ye-Gelfand.pdfen
dc.identifier.urihttp://hdl.handle.net/10919/56706en
dc.identifier.urlhttp://www.imaging.sbes.vt.edu/posters/Poster-Ye-Gelfand.pdfen
dc.language.isoen_USen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectInversion formulasen
dc.subjectX-raysen
dc.subjectTomographyen
dc.titleGel'fand-Graev's Reconstruction Formula in the 3D Real Space - a Framework towards a General Interior Tomography Theoryen
dc.typePosteren
dc.type.dcmitypeTexten

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