Statistical Regularization of Inverse Problems
In experimental sciences we often need to solve inverse problems. That is, we want to obtain information about the internal structure of a physical system from indirect noisy observations. Often the problem is not whether a solution exists; on the contrary, there are too many solutions that fit the...
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| Veröffentlicht in: | SIAM review 2001, Vol.43 (2), p.347-366 |
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| container_title | SIAM review |
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| creator | Tenorio, Luis |
| description | In experimental sciences we often need to solve inverse problems. That is, we want to obtain information about the internal structure of a physical system from indirect noisy observations. Often the problem is not whether a solution exists; on the contrary, there are too many solutions that fit the data to a chosen tolerance level. The goal is to use prior information to determine a physically meaningful solution. Here, we present some of the basic questions that arise. We describe methods that can be used to find inversion estimates as well as ways to assess their performance. |
| doi_str_mv | 10.1137/s0036144500358232 |
| format | Article |
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We describe methods that can be used to find inversion estimates as well as ways to assess their performance.</description><subject>Approximations and expansions</subject><subject>Confidence interval</subject><subject>Cosmic microwave background radiation</subject><subject>Data smoothing</subject><subject>Education</subject><subject>Estimation bias</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>Integral equations</subject><subject>Inverse problems</subject><subject>Linear inference, regression</subject><subject>Mathematical analysis</subject><subject>Mathematical functions</subject><subject>Mathematical vectors</subject><subject>Mathematics</subject><subject>Minimax</subject><subject>Nonparametric inference</subject><subject>Probability and statistics</subject><subject>Problem solving</subject><subject>Sciences and techniques of general use</subject><subject>Statistical variance</subject><subject>Statistics</subject><issn>0036-1445</issn><issn>1095-7200</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNpdkEFLxDAQhYMoWFd_gOChiNeuSZNJ2qMsri4sKK6eS5qm0tJt1kwr6K83ZRcRT4-Z980bZgi5ZHTOGFe3SCmXTAgIClnK0yMSMZpDolJKj0k02cnkn5IzxJaGOuN5ROabQQ8NDo3RXfxi38dO--Y7tFwfuzpe9Z_Wo42fvSs7u8VzclLrDu3FQWfkbXn_unhM1k8Pq8XdOjFC8iGBSmpR2pSD0DYDVUlmswqM1BpqmdHMVoJXlUqVUdRIqSXwvFQK6lKKlHI-I9f73J13H6PFoWjd6PuwsmB5IAQABIjtIeMdord1sfPNVvuvgtFi-kqx-f-VMHNzCNYYTq697k2DfwYh58ACdrXHWhyc_7W5FLkKxA-ZlWky</recordid><startdate>2001</startdate><enddate>2001</enddate><creator>Tenorio, Luis</creator><general>Society for Industrial and Applied Mathematics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><scope>U9A</scope></search><sort><creationdate>2001</creationdate><title>Statistical Regularization of Inverse Problems</title><author>Tenorio, Luis</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c463t-5d6a4be2354ae857d61e8d5c6aa5f6808ed43dd727c70c66a6539b775fb642033</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Approximations and expansions</topic><topic>Confidence interval</topic><topic>Cosmic microwave background radiation</topic><topic>Data smoothing</topic><topic>Education</topic><topic>Estimation bias</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>Integral equations</topic><topic>Inverse problems</topic><topic>Linear inference, regression</topic><topic>Mathematical analysis</topic><topic>Mathematical functions</topic><topic>Mathematical vectors</topic><topic>Mathematics</topic><topic>Minimax</topic><topic>Nonparametric inference</topic><topic>Probability and statistics</topic><topic>Problem solving</topic><topic>Sciences and techniques of general use</topic><topic>Statistical variance</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tenorio, Luis</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>SIAM review</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tenorio, Luis</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Statistical Regularization of Inverse Problems</atitle><jtitle>SIAM review</jtitle><date>2001</date><risdate>2001</risdate><volume>43</volume><issue>2</issue><spage>347</spage><epage>366</epage><pages>347-366</pages><issn>0036-1445</issn><eissn>1095-7200</eissn><coden>SIREAD</coden><abstract>In experimental sciences we often need to solve inverse problems. 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| fulltext | fulltext |
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| ispartof | SIAM review, 2001, Vol.43 (2), p.347-366 |
| issn | 0036-1445 1095-7200 |
| language | eng |
| recordid | cdi_proquest_journals_194204555 |
| source | Jstor Complete Legacy; LOCUS - SIAM's Online Journal Archive; JSTOR Mathematics & Statistics; EBSCOhost Business Source Complete |
| subjects | Approximations and expansions Confidence interval Cosmic microwave background radiation Data smoothing Education Estimation bias Estimators Exact sciences and technology Integral equations Inverse problems Linear inference, regression Mathematical analysis Mathematical functions Mathematical vectors Mathematics Minimax Nonparametric inference Probability and statistics Problem solving Sciences and techniques of general use Statistical variance Statistics |
| title | Statistical Regularization of Inverse Problems |
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