Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix
The generalized Landweber iteration with a variable shaping matrix is used to solve the large linear system of equations arising in the image reconstruction problem of emission tomography. The method is based on the property that once a spatial frequency image component is almost recovered within in...
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| Veröffentlicht in: | IEEE transactions on medical imaging 1993-06, Vol.12 (2), p.278-286 |
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| container_end_page | 286 |
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| container_title | IEEE transactions on medical imaging |
| container_volume | 12 |
| creator | Pan, T.-S. Yagle, A.E. Clinthorne, N.H. Rogers, W.L. |
| description | The generalized Landweber iteration with a variable shaping matrix is used to solve the large linear system of equations arising in the image reconstruction problem of emission tomography. The method is based on the property that once a spatial frequency image component is almost recovered within in in the generalized Landweber iteration, this component will still stay within in during subsequent iterations with a different shaping matrix, as long as this shaping matrix satisfies the convergence criterion for the component. Two different shaping matrices are used: the first recovers low-frequency image components; and the second may be used either to accelerate the reconstruction of high-frequency image components, or to attenuate these components to filter the image. The variable shaping matrix gives results similar to truncated inverse filtering, but requires much less computation and memory, since it does not rely on the singular value decomposition.< > |
| doi_str_mv | 10.1109/42.232256 |
| format | Article |
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The method is based on the property that once a spatial frequency image component is almost recovered within in in the generalized Landweber iteration, this component will still stay within in during subsequent iterations with a different shaping matrix, as long as this shaping matrix satisfies the convergence criterion for the component. Two different shaping matrices are used: the first recovers low-frequency image components; and the second may be used either to accelerate the reconstruction of high-frequency image components, or to attenuate these components to filter the image. The variable shaping matrix gives results similar to truncated inverse filtering, but requires much less computation and memory, since it does not rely on the singular value decomposition.< ></description><identifier>ISSN: 0278-0062</identifier><identifier>EISSN: 1558-254X</identifier><identifier>DOI: 10.1109/42.232256</identifier><identifier>PMID: 18218415</identifier><identifier>CODEN: ITMID4</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>550601 - Medicine- Unsealed Radionuclides in Diagnostics ; Acceleration ; ACCURACY ; ATTENUATION ; Biological and medical sciences ; COMPUTERIZED TOMOGRAPHY ; Convergence ; DIAGNOSTIC TECHNIQUES ; EQUATIONS ; Filtering ; Filters ; Frequency ; IMAGE PROCESSING ; Image reconstruction ; Investigative techniques, diagnostic techniques (general aspects) ; Linear systems ; Matrix decomposition ; Medical sciences ; Miscellaneous. Technology ; PROCESSING ; RADIOLOGY AND NUCLEAR MEDICINE ; Radionuclide investigations ; RESOLUTION ; SPATIAL RESOLUTION ; TOMOGRAPHY</subject><ispartof>IEEE transactions on medical imaging, 1993-06, Vol.12 (2), p.278-286</ispartof><rights>1993 INIST-CNRS</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c450t-e7593a0d0244bb539f0a69bf61cee6095e4168c350b24eaa7da775d70a7efd503</citedby><cites>FETCH-LOGICAL-c450t-e7593a0d0244bb539f0a69bf61cee6095e4168c350b24eaa7da775d70a7efd503</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/232256$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>230,314,780,784,796,885,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/232256$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=4888056$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/18218415$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink><backlink>$$Uhttps://www.osti.gov/biblio/5953432$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Pan, T.-S.</creatorcontrib><creatorcontrib>Yagle, A.E.</creatorcontrib><creatorcontrib>Clinthorne, N.H.</creatorcontrib><creatorcontrib>Rogers, W.L.</creatorcontrib><title>Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix</title><title>IEEE transactions on medical imaging</title><addtitle>TMI</addtitle><addtitle>IEEE Trans Med Imaging</addtitle><description>The generalized Landweber iteration with a variable shaping matrix is used to solve the large linear system of equations arising in the image reconstruction problem of emission tomography. The method is based on the property that once a spatial frequency image component is almost recovered within in in the generalized Landweber iteration, this component will still stay within in during subsequent iterations with a different shaping matrix, as long as this shaping matrix satisfies the convergence criterion for the component. Two different shaping matrices are used: the first recovers low-frequency image components; and the second may be used either to accelerate the reconstruction of high-frequency image components, or to attenuate these components to filter the image. The variable shaping matrix gives results similar to truncated inverse filtering, but requires much less computation and memory, since it does not rely on the singular value decomposition.< ></description><subject>550601 - Medicine- Unsealed Radionuclides in Diagnostics</subject><subject>Acceleration</subject><subject>ACCURACY</subject><subject>ATTENUATION</subject><subject>Biological and medical sciences</subject><subject>COMPUTERIZED TOMOGRAPHY</subject><subject>Convergence</subject><subject>DIAGNOSTIC TECHNIQUES</subject><subject>EQUATIONS</subject><subject>Filtering</subject><subject>Filters</subject><subject>Frequency</subject><subject>IMAGE PROCESSING</subject><subject>Image reconstruction</subject><subject>Investigative techniques, diagnostic techniques (general aspects)</subject><subject>Linear systems</subject><subject>Matrix decomposition</subject><subject>Medical sciences</subject><subject>Miscellaneous. Technology</subject><subject>PROCESSING</subject><subject>RADIOLOGY AND NUCLEAR MEDICINE</subject><subject>Radionuclide investigations</subject><subject>RESOLUTION</subject><subject>SPATIAL RESOLUTION</subject><subject>TOMOGRAPHY</subject><issn>0278-0062</issn><issn>1558-254X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1993</creationdate><recordtype>article</recordtype><recordid>eNqF0UFvFCEUB3BiNHZdPXj1YIgxNh6mAgMMHJtGrckmXjTxNnnDvOliZpkV2Gr99LLOtN7siYT34_HPe4Q85-yMc2bfSXEmaiGUfkBWXClTCSW_PSQrJhpTMabFCXmS0nfGuFTMPiYn3AhuJFcrAufO4YgRsp8ChdDTwY8Zow9X1Aeat0ivMJT66H9jTzdF_MQOI_X59tEhHTHQa4geuhFp2sL-eLWDHP2vp-TRAGPCZ8u5Jl8_vP9ycVltPn_8dHG-qVwJlStslK2B9UxI2XWqtgMDbbtBc4eomVUouTauVqwTEgGaHppG9Q2DBodesXpNXs19p5R9m1wJ6LZuCgFdbpVVtaxFQacz2sfpxwFTbnc-lQGMEHA6pLappZBalChr8ua_UhhueYl5P1RW68ayeyHX2kitVIFvZ-jilFLEod1Hv4N403LWHhfeStHOCy_25dL00O2w_yeXDRfwegGQHIxDhOB8unPSGMP-9nkxM4-Id9Xlkz9OWbmi</recordid><startdate>19930601</startdate><enddate>19930601</enddate><creator>Pan, T.-S.</creator><creator>Yagle, A.E.</creator><creator>Clinthorne, N.H.</creator><creator>Rogers, W.L.</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>7QO</scope><scope>8FD</scope><scope>FR3</scope><scope>P64</scope><scope>7SC</scope><scope>7SP</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7U5</scope><scope>7X8</scope><scope>OTOTI</scope></search><sort><creationdate>19930601</creationdate><title>Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix</title><author>Pan, T.-S. ; Yagle, A.E. ; Clinthorne, N.H. ; Rogers, W.L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c450t-e7593a0d0244bb539f0a69bf61cee6095e4168c350b24eaa7da775d70a7efd503</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1993</creationdate><topic>550601 - Medicine- Unsealed Radionuclides in Diagnostics</topic><topic>Acceleration</topic><topic>ACCURACY</topic><topic>ATTENUATION</topic><topic>Biological and medical sciences</topic><topic>COMPUTERIZED TOMOGRAPHY</topic><topic>Convergence</topic><topic>DIAGNOSTIC TECHNIQUES</topic><topic>EQUATIONS</topic><topic>Filtering</topic><topic>Filters</topic><topic>Frequency</topic><topic>IMAGE PROCESSING</topic><topic>Image reconstruction</topic><topic>Investigative techniques, diagnostic techniques (general aspects)</topic><topic>Linear systems</topic><topic>Matrix decomposition</topic><topic>Medical sciences</topic><topic>Miscellaneous. Technology</topic><topic>PROCESSING</topic><topic>RADIOLOGY AND NUCLEAR MEDICINE</topic><topic>Radionuclide investigations</topic><topic>RESOLUTION</topic><topic>SPATIAL RESOLUTION</topic><topic>TOMOGRAPHY</topic><toplevel>online_resources</toplevel><creatorcontrib>Pan, T.-S.</creatorcontrib><creatorcontrib>Yagle, A.E.</creatorcontrib><creatorcontrib>Clinthorne, N.H.</creatorcontrib><creatorcontrib>Rogers, W.L.</creatorcontrib><collection>Pascal-Francis</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Biotechnology Research Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</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>Solid State and Superconductivity Abstracts</collection><collection>MEDLINE - Academic</collection><collection>OSTI.GOV</collection><jtitle>IEEE transactions on medical imaging</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Pan, T.-S.</au><au>Yagle, A.E.</au><au>Clinthorne, N.H.</au><au>Rogers, W.L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix</atitle><jtitle>IEEE transactions on medical imaging</jtitle><stitle>TMI</stitle><addtitle>IEEE Trans Med Imaging</addtitle><date>1993-06-01</date><risdate>1993</risdate><volume>12</volume><issue>2</issue><spage>278</spage><epage>286</epage><pages>278-286</pages><issn>0278-0062</issn><eissn>1558-254X</eissn><coden>ITMID4</coden><abstract>The generalized Landweber iteration with a variable shaping matrix is used to solve the large linear system of equations arising in the image reconstruction problem of emission tomography. The method is based on the property that once a spatial frequency image component is almost recovered within in in the generalized Landweber iteration, this component will still stay within in during subsequent iterations with a different shaping matrix, as long as this shaping matrix satisfies the convergence criterion for the component. Two different shaping matrices are used: the first recovers low-frequency image components; and the second may be used either to accelerate the reconstruction of high-frequency image components, or to attenuate these components to filter the image. The variable shaping matrix gives results similar to truncated inverse filtering, but requires much less computation and memory, since it does not rely on the singular value decomposition.< ></abstract><cop>New York, NY</cop><pub>IEEE</pub><pmid>18218415</pmid><doi>10.1109/42.232256</doi><tpages>9</tpages></addata></record> |
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| ispartof | IEEE transactions on medical imaging, 1993-06, Vol.12 (2), p.278-286 |
| issn | 0278-0062 1558-254X |
| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | 550601 - Medicine- Unsealed Radionuclides in Diagnostics Acceleration ACCURACY ATTENUATION Biological and medical sciences COMPUTERIZED TOMOGRAPHY Convergence DIAGNOSTIC TECHNIQUES EQUATIONS Filtering Filters Frequency IMAGE PROCESSING Image reconstruction Investigative techniques, diagnostic techniques (general aspects) Linear systems Matrix decomposition Medical sciences Miscellaneous. Technology PROCESSING RADIOLOGY AND NUCLEAR MEDICINE Radionuclide investigations RESOLUTION SPATIAL RESOLUTION TOMOGRAPHY |
| title | Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix |
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