A derivative-free noncircular fan-beam reconstruction formula
In order to perform fan-beam reconstruction using projection data collected from a noncircular scanning locus, existing noncircular fan-beam formulas require a derivative of the scanning locus with respect to the rotation angle. A derivative-free noncircular fan-beam reconstruction formula that is b...
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| Veröffentlicht in: | IEEE transactions on image processing 1993-10, Vol.2 (4), p.543-547 |
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| container_title | IEEE transactions on image processing |
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| creator | Wang, G. Lin, T.-H. Cheng, P.-C. |
| description | In order to perform fan-beam reconstruction using projection data collected from a noncircular scanning locus, existing noncircular fan-beam formulas require a derivative of the scanning locus with respect to the rotation angle. A derivative-free noncircular fan-beam reconstruction formula that is based on a geometrical explanation of the circular equispatial fan-beam reconstruction formula is obtained here. A mathematical proof is then provided under the conditions that the source-to-origin distance is symmetric with respect to the origin of the reconstruction coordinate system, is differentiable almost everywhere, and does not change too fast with respect to the rotation angle. The derivative-free noncircular fan-beam reconstruction formula is the same as the circular one, except that the source-to-origin distance is a function of the rotation angle. A typical simulation result for the noncircular fan-beam formula is given.< > |
| doi_str_mv | 10.1109/83.242365 |
| format | Article |
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A derivative-free noncircular fan-beam reconstruction formula that is based on a geometrical explanation of the circular equispatial fan-beam reconstruction formula is obtained here. A mathematical proof is then provided under the conditions that the source-to-origin distance is symmetric with respect to the origin of the reconstruction coordinate system, is differentiable almost everywhere, and does not change too fast with respect to the rotation angle. The derivative-free noncircular fan-beam reconstruction formula is the same as the circular one, except that the source-to-origin distance is a function of the rotation angle. A typical simulation result for the noncircular fan-beam formula is given.< ></description><identifier>ISSN: 1057-7149</identifier><identifier>EISSN: 1941-0042</identifier><identifier>DOI: 10.1109/83.242365</identifier><identifier>PMID: 18296240</identifier><identifier>CODEN: IIPRE4</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Applied sciences ; Biological materials ; Biomedical engineering ; Biomedical materials ; Detectors ; Exact sciences and technology ; Image processing ; Image reconstruction ; Information, signal and communications theory ; Laboratories ; Radiology ; Real time systems ; Sensor arrays ; Signal processing ; Synchrotron radiation ; Telecommunications and information theory</subject><ispartof>IEEE transactions on image processing, 1993-10, Vol.2 (4), p.543-547</ispartof><rights>1994 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c361t-abe01cbcede0ac2781d198197ee246c4874b717c9698740253ca5487a14514df3</citedby><cites>FETCH-LOGICAL-c361t-abe01cbcede0ac2781d198197ee246c4874b717c9698740253ca5487a14514df3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/242365$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54736</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/242365$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=3806092$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/18296240$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Wang, G.</creatorcontrib><creatorcontrib>Lin, T.-H.</creatorcontrib><creatorcontrib>Cheng, P.-C.</creatorcontrib><title>A derivative-free noncircular fan-beam reconstruction formula</title><title>IEEE transactions on image processing</title><addtitle>TIP</addtitle><addtitle>IEEE Trans Image Process</addtitle><description>In order to perform fan-beam reconstruction using projection data collected from a noncircular scanning locus, existing noncircular fan-beam formulas require a derivative of the scanning locus with respect to the rotation angle. A derivative-free noncircular fan-beam reconstruction formula that is based on a geometrical explanation of the circular equispatial fan-beam reconstruction formula is obtained here. A mathematical proof is then provided under the conditions that the source-to-origin distance is symmetric with respect to the origin of the reconstruction coordinate system, is differentiable almost everywhere, and does not change too fast with respect to the rotation angle. The derivative-free noncircular fan-beam reconstruction formula is the same as the circular one, except that the source-to-origin distance is a function of the rotation angle. A typical simulation result for the noncircular fan-beam formula is given.< ></description><subject>Applied sciences</subject><subject>Biological materials</subject><subject>Biomedical engineering</subject><subject>Biomedical materials</subject><subject>Detectors</subject><subject>Exact sciences and technology</subject><subject>Image processing</subject><subject>Image reconstruction</subject><subject>Information, signal and communications theory</subject><subject>Laboratories</subject><subject>Radiology</subject><subject>Real time systems</subject><subject>Sensor arrays</subject><subject>Signal processing</subject><subject>Synchrotron radiation</subject><subject>Telecommunications and information theory</subject><issn>1057-7149</issn><issn>1941-0042</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1993</creationdate><recordtype>article</recordtype><recordid>eNp90E1LxDAQBuAgiruuHrx6kB5E8dA1k6RNcvCwLH7Bghc9lzSdQqUfa9Iu-O_N0rLePGXIPMwMLyGXQJcAVD8ovmSC8TQ5InPQAmJKBTsONU1kLEHoGTnz_otSEAmkp2QGiumUCTonj6uoQFftTF_tMC4dYtR2ra2cHWrjotK0cY6miRzarvW9G2xfdW1Udq4J4JyclKb2eDG9C_L5_PSxfo037y9v69UmtjyFPjY5UrC5xQKpsUwqKEAr0BKRidQKJUUuQVqd6lBSlnBrkvBr9veKouQLcjfO3brue0DfZ03lLda1abEbfCa5YJKmVAd5-69kinHBRRrg_Qit67x3WGZbVzXG_WRAs32qmeLZmGqw19PQIW-w-JNTjAHcTMB4a-rSmRChPziu9rexwK5GViHioTst-QXzjIVL</recordid><startdate>19931001</startdate><enddate>19931001</enddate><creator>Wang, G.</creator><creator>Lin, T.-H.</creator><creator>Cheng, P.-C.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>IQODW</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7X8</scope></search><sort><creationdate>19931001</creationdate><title>A derivative-free noncircular fan-beam reconstruction formula</title><author>Wang, G. ; Lin, T.-H. ; Cheng, P.-C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c361t-abe01cbcede0ac2781d198197ee246c4874b717c9698740253ca5487a14514df3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1993</creationdate><topic>Applied sciences</topic><topic>Biological materials</topic><topic>Biomedical engineering</topic><topic>Biomedical materials</topic><topic>Detectors</topic><topic>Exact sciences and technology</topic><topic>Image processing</topic><topic>Image reconstruction</topic><topic>Information, signal and communications theory</topic><topic>Laboratories</topic><topic>Radiology</topic><topic>Real time systems</topic><topic>Sensor arrays</topic><topic>Signal processing</topic><topic>Synchrotron radiation</topic><topic>Telecommunications and information theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, G.</creatorcontrib><creatorcontrib>Lin, T.-H.</creatorcontrib><creatorcontrib>Cheng, P.-C.</creatorcontrib><collection>Pascal-Francis</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>MEDLINE - Academic</collection><jtitle>IEEE transactions on image processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Wang, G.</au><au>Lin, T.-H.</au><au>Cheng, P.-C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A derivative-free noncircular fan-beam reconstruction formula</atitle><jtitle>IEEE transactions on image processing</jtitle><stitle>TIP</stitle><addtitle>IEEE Trans Image Process</addtitle><date>1993-10-01</date><risdate>1993</risdate><volume>2</volume><issue>4</issue><spage>543</spage><epage>547</epage><pages>543-547</pages><issn>1057-7149</issn><eissn>1941-0042</eissn><coden>IIPRE4</coden><abstract>In order to perform fan-beam reconstruction using projection data collected from a noncircular scanning locus, existing noncircular fan-beam formulas require a derivative of the scanning locus with respect to the rotation angle. A derivative-free noncircular fan-beam reconstruction formula that is based on a geometrical explanation of the circular equispatial fan-beam reconstruction formula is obtained here. A mathematical proof is then provided under the conditions that the source-to-origin distance is symmetric with respect to the origin of the reconstruction coordinate system, is differentiable almost everywhere, and does not change too fast with respect to the rotation angle. The derivative-free noncircular fan-beam reconstruction formula is the same as the circular one, except that the source-to-origin distance is a function of the rotation angle. A typical simulation result for the noncircular fan-beam formula is given.< ></abstract><cop>New York, NY</cop><pub>IEEE</pub><pmid>18296240</pmid><doi>10.1109/83.242365</doi><tpages>5</tpages></addata></record> |
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| ispartof | IEEE transactions on image processing, 1993-10, Vol.2 (4), p.543-547 |
| issn | 1057-7149 1941-0042 |
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| source | IEEE Xplore |
| subjects | Applied sciences Biological materials Biomedical engineering Biomedical materials Detectors Exact sciences and technology Image processing Image reconstruction Information, signal and communications theory Laboratories Radiology Real time systems Sensor arrays Signal processing Synchrotron radiation Telecommunications and information theory |
| title | A derivative-free noncircular fan-beam reconstruction formula |
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