Paired Transform Slice Theorem of 2-D Image Reconstruction from Projections
This paper discusses the paired transform-based method of reconstruction of 2-D images from their projections. The complete set of basic functions of the 2-D discrete paired transform are defined by specific directions, i.e. the transform is directional and can be calculated from the projection data...
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| creator | Dursun, Serkan Nan Du Grigoryan, Artyom M |
| description | This paper discusses the paired transform-based method of reconstruction of 2-D images from their projections. The complete set of basic functions of the 2-D discrete paired transform are defined by specific directions, i.e. the transform is directional and can be calculated from the projection data. A simple formula is presented for image reconstruction without calculating the 2-D discrete Fourier transform in the case, when the size of image is L r × L r , when L is prime. The image reconstruction is described by the discrete model that is used in the series expansion methods of image reconstruction. The proposed method of reconstruction has been implemented and successfully applied for modeled images on Cartesian grid of sizes up to 256×256. |
| doi_str_mv | 10.1109/ICPR.2010.586 |
| format | Conference Proceeding |
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The complete set of basic functions of the 2-D discrete paired transform are defined by specific directions, i.e. the transform is directional and can be calculated from the projection data. A simple formula is presented for image reconstruction without calculating the 2-D discrete Fourier transform in the case, when the size of image is L r × L r , when L is prime. The image reconstruction is described by the discrete model that is used in the series expansion methods of image reconstruction. The proposed method of reconstruction has been implemented and successfully applied for modeled images on Cartesian grid of sizes up to 256×256.</description><subject>Discrete Fourier transforms</subject><subject>Generators</subject><subject>Head</subject><subject>Image reconstruction</subject><subject>Image restoration and reconstruction</subject><subject>Mathematical model</subject><subject>paired transform</subject><subject>signal/image representation</subject><subject>Tomography</subject><issn>1051-4651</issn><issn>2831-7475</issn><isbn>1424475422</isbn><isbn>9781424475421</isbn><isbn>9781424475414</isbn><isbn>9780769541099</isbn><isbn>1424475414</isbn><isbn>0769541097</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2010</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNo1zMtOwzAQhWFzkyglS1Zs_AIptuOJ4yUKBSoqUZXsq4kzBqMmRk5Y8PZUXFZHn470M3YlxUJKYW9W9Wa7UOJAqMojlllTSa20NqClPmYzVRUyNweesIv_Q6lTNpMCZK5LkOcsG8fQClWa0gDAjD1tMCTqeJNwGH1MPX_ZB0e8eaOYqOfRc5Xf8VWPr8S35OIwTunTTSEO3KfY802K7_Tj8ZKdedyPlP3tnDX3y6Z-zNfPD6v6dp0HK6acWqdR2Ba7UlhtneiMb9GYwhlEACOcQ-F8R2Sd9x7QOSU7UQHIAgupijm7_s0GItp9pNBj-toBWDC2LL4B1iNSIw</recordid><startdate>201008</startdate><enddate>201008</enddate><creator>Dursun, Serkan</creator><creator>Nan Du</creator><creator>Grigoryan, Artyom M</creator><general>IEEE</general><scope>6IE</scope><scope>6IL</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIL</scope></search><sort><creationdate>201008</creationdate><title>Paired Transform Slice Theorem of 2-D Image Reconstruction from Projections</title><author>Dursun, Serkan ; Nan Du ; Grigoryan, Artyom M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i90t-ebc4a09bad60949c0d7fba773c7aa5570cca0cfdee9cfff5acc21d085513a3123</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Discrete Fourier transforms</topic><topic>Generators</topic><topic>Head</topic><topic>Image reconstruction</topic><topic>Image restoration and reconstruction</topic><topic>Mathematical model</topic><topic>paired transform</topic><topic>signal/image representation</topic><topic>Tomography</topic><toplevel>online_resources</toplevel><creatorcontrib>Dursun, Serkan</creatorcontrib><creatorcontrib>Nan Du</creatorcontrib><creatorcontrib>Grigoryan, Artyom M</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan All Online (POP All Online) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP All) 1998-Present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Dursun, Serkan</au><au>Nan Du</au><au>Grigoryan, Artyom M</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Paired Transform Slice Theorem of 2-D Image Reconstruction from Projections</atitle><btitle>2010 20th International Conference on Pattern Recognition</btitle><stitle>ICPR</stitle><date>2010-08</date><risdate>2010</risdate><spage>2395</spage><epage>2398</epage><pages>2395-2398</pages><issn>1051-4651</issn><eissn>2831-7475</eissn><isbn>1424475422</isbn><isbn>9781424475421</isbn><eisbn>9781424475414</eisbn><eisbn>9780769541099</eisbn><eisbn>1424475414</eisbn><eisbn>0769541097</eisbn><abstract>This paper discusses the paired transform-based method of reconstruction of 2-D images from their projections. The complete set of basic functions of the 2-D discrete paired transform are defined by specific directions, i.e. the transform is directional and can be calculated from the projection data. A simple formula is presented for image reconstruction without calculating the 2-D discrete Fourier transform in the case, when the size of image is L r × L r , when L is prime. The image reconstruction is described by the discrete model that is used in the series expansion methods of image reconstruction. The proposed method of reconstruction has been implemented and successfully applied for modeled images on Cartesian grid of sizes up to 256×256.</abstract><pub>IEEE</pub><doi>10.1109/ICPR.2010.586</doi><tpages>4</tpages></addata></record> |
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| issn | 1051-4651 2831-7475 |
| language | eng |
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| source | IEEE Electronic Library (IEL) Conference Proceedings |
| subjects | Discrete Fourier transforms Generators Head Image reconstruction Image restoration and reconstruction Mathematical model paired transform signal/image representation Tomography |
| title | Paired Transform Slice Theorem of 2-D Image Reconstruction from Projections |
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