Bayesian and regularization methods for hyperparameter estimation in image restoration
In this paper, we propose the application of the hierarchical Bayesian paradigm to the image restoration problem. We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian paradigm. We...
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| Veröffentlicht in: | IEEE transactions on image processing 1999-02, Vol.8 (2), p.231-246 |
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| container_title | IEEE transactions on image processing |
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| creator | Molina, R. Katsaggelos, A.K. Mateos, J. |
| description | In this paper, we propose the application of the hierarchical Bayesian paradigm to the image restoration problem. We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian paradigm. We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the image restoration problem. We furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters, or their ratio, defined as the regularization parameter. Finally the proposed algorithms are tested experimentally. |
| doi_str_mv | 10.1109/83.743857 |
| format | Article |
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We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian paradigm. We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the image restoration problem. We furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters, or their ratio, defined as the regularization parameter. Finally the proposed algorithms are tested experimentally.</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Bayesian analysis</subject><subject>Bayesian methods</subject><subject>Degradation</subject><subject>Estimating</subject><subject>Exact sciences and technology</subject><subject>Image analysis</subject><subject>Image processing</subject><subject>Image restoration</subject><subject>Information, signal and communications theory</subject><subject>Iterative algorithms</subject><subject>Iterative methods</subject><subject>Lead</subject><subject>Least squares approximation</subject><subject>Mathematical analysis</subject><subject>Parameter estimation</subject><subject>Regularization</subject><subject>Signal processing</subject><subject>Telecommunications and information theory</subject><subject>Testing</subject><issn>1057-7149</issn><issn>1941-0042</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqF0b1v1TAQAHALUdEPGFgZUAZE2yHlznF89ghVaStVYgHWyEnObVA-Hnbe8PrX120iuhXJku3zz3eyT4j3CGeIYL-Y4oxUYUp6JQ7QKswBlHyd1lBSTqjsvjiM8Q8AqhL1G7GPRmpSBAfi9ze349i5MXNjmwW-3fYudPdu7qYxG3i-m9qY-Slkd7sNh40LLgU5ZBznblhUl8bgbjndjvMUnoJvxZ53feR363wkfn2_-Hl-ld_8uLw-_3qTN8rinHPtnJEle12Dka0no1uoy5KsJNBEXDMgaC-prb2VVmmbdjUpBaoBj8WROF7ybsL0d5vqV0MXG-57N_K0jRUVCo1BoCQ_vyilQSu10v-H2mhD9jHjyYsQNWFB6dPLRE8X2oQpxsC-2oT0Z2FXIVSPLaxMUS0tTPbjmnZbD9w-y7VnCXxagYuN631wY9PFZ6d1kZ6R2IeFdcz873Qt8gC5iqqo</recordid><startdate>19990201</startdate><enddate>19990201</enddate><creator>Molina, R.</creator><creator>Katsaggelos, A.K.</creator><creator>Mateos, J.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>F28</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7X8</scope></search><sort><creationdate>19990201</creationdate><title>Bayesian and regularization methods for hyperparameter estimation in image restoration</title><author>Molina, R. ; Katsaggelos, A.K. ; Mateos, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c491t-ebaa825ef6b082df786d0b5579270677ebe0106f27dbf92946906fb74404c0f13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Bayesian analysis</topic><topic>Bayesian methods</topic><topic>Degradation</topic><topic>Estimating</topic><topic>Exact sciences and technology</topic><topic>Image analysis</topic><topic>Image processing</topic><topic>Image restoration</topic><topic>Information, signal and communications theory</topic><topic>Iterative algorithms</topic><topic>Iterative methods</topic><topic>Lead</topic><topic>Least squares approximation</topic><topic>Mathematical analysis</topic><topic>Parameter estimation</topic><topic>Regularization</topic><topic>Signal processing</topic><topic>Telecommunications and information theory</topic><topic>Testing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Molina, R.</creatorcontrib><creatorcontrib>Katsaggelos, A.K.</creatorcontrib><creatorcontrib>Mateos, J.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering 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>Molina, R.</au><au>Katsaggelos, A.K.</au><au>Mateos, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bayesian and regularization methods for hyperparameter estimation in image restoration</atitle><jtitle>IEEE transactions on image processing</jtitle><stitle>TIP</stitle><addtitle>IEEE Trans Image Process</addtitle><date>1999-02-01</date><risdate>1999</risdate><volume>8</volume><issue>2</issue><spage>231</spage><epage>246</epage><pages>231-246</pages><issn>1057-7149</issn><eissn>1941-0042</eissn><coden>IIPRE4</coden><abstract>In this paper, we propose the application of the hierarchical Bayesian paradigm to the image restoration problem. We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian paradigm. We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the image restoration problem. We furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters, or their ratio, defined as the regularization parameter. Finally the proposed algorithms are tested experimentally.</abstract><cop>New York, NY</cop><pub>IEEE</pub><pmid>18267470</pmid><doi>10.1109/83.743857</doi><tpages>16</tpages></addata></record> |
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| ispartof | IEEE transactions on image processing, 1999-02, Vol.8 (2), p.231-246 |
| issn | 1057-7149 1941-0042 |
| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Algorithms Applied sciences Bayesian analysis Bayesian methods Degradation Estimating Exact sciences and technology Image analysis Image processing Image restoration Information, signal and communications theory Iterative algorithms Iterative methods Lead Least squares approximation Mathematical analysis Parameter estimation Regularization Signal processing Telecommunications and information theory Testing |
| title | Bayesian and regularization methods for hyperparameter estimation in image restoration |
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