Robust Subspace Detectors Based on α-Divergence With Application to Detection in Imaging
Robust variants of Wald, Rao and likelihood ratio (LR) tests for the detection of a signal subspace in a signal interference subspace corrupted by contaminated Gaussian noise are proposed in this paper. They are derived using the \alpha - divergence, and the trade-off between the robustness and the...
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| Veröffentlicht in: | IEEE transactions on image processing 2021-01, Vol.30, p.5017-5031 |
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| creator | Rekavandi, Aref Miri Seghouane, Abd-Krim Evans, Robin J. |
| description | Robust variants of Wald, Rao and likelihood ratio (LR) tests for the detection of a signal subspace in a signal interference subspace corrupted by contaminated Gaussian noise are proposed in this paper. They are derived using the \alpha - divergence, and the trade-off between the robustness and the power (the probability of detection) of the tests is adjustable using a single hyperparameter \alpha . It is shown that when \alpha \rightarrow 1 , these tests are equivalent to their well known classical counterparts. For example the robust LR test coincides with the LR test or the matched subspace detector (MSD). Asymptotic results are provided to support the proposed tests and robustness to outliers is obtained using values of \alpha < 1 . Numerical experiments illustrating the performance of these tests on simulated, real functional magnetic resonance imaging (fMRI), hyperspectral and synthetic aperture radar (SAR) data are also presented. |
| doi_str_mv | 10.1109/TIP.2021.3077139 |
| format | Article |
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They are derived using the <inline-formula> <tex-math notation="LaTeX">\alpha - </tex-math></inline-formula>divergence, and the trade-off between the robustness and the power (the probability of detection) of the tests is adjustable using a single hyperparameter <inline-formula> <tex-math notation="LaTeX">\alpha </tex-math></inline-formula>. It is shown that when <inline-formula> <tex-math notation="LaTeX">\alpha \rightarrow 1 </tex-math></inline-formula>, these tests are equivalent to their well known classical counterparts. For example the robust LR test coincides with the LR test or the matched subspace detector (MSD). Asymptotic results are provided to support the proposed tests and robustness to outliers is obtained using values of <inline-formula> <tex-math notation="LaTeX">\alpha < 1 </tex-math></inline-formula>. Numerical experiments illustrating the performance of these tests on simulated, real functional magnetic resonance imaging (fMRI), hyperspectral and synthetic aperture radar (SAR) data are also presented.]]></description><identifier>ISSN: 1057-7149</identifier><identifier>EISSN: 1941-0042</identifier><identifier>DOI: 10.1109/TIP.2021.3077139</identifier><identifier>PMID: 33961559</identifier><identifier>CODEN: IIPRE4</identifier><language>eng</language><publisher>United States: IEEE</publisher><subject><italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α -divergence ; Detectors ; Gaussian noise ; Light rail systems ; Likelihood ratio ; likelihood ratio test ; Magnetic resonance imaging ; Maximum likelihood estimation ; Outliers (statistics) ; Pollution measurement ; Random noise ; Rao test ; Robust detection ; Robustness ; Robustness (mathematics) ; subspace detectors ; Subspaces ; Synthetic aperture radar ; Uncertainty ; Wald test</subject><ispartof>IEEE transactions on image processing, 2021-01, Vol.30, p.5017-5031</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c347t-8bbcfa1a232050a41adbc3e6f930be976b12b6c9eef2d8f2311b8b908cd5a71e3</citedby><cites>FETCH-LOGICAL-c347t-8bbcfa1a232050a41adbc3e6f930be976b12b6c9eef2d8f2311b8b908cd5a71e3</cites><orcidid>0000-0001-9542-759X ; 0000-0003-4619-734X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/9426446$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/9426446$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/33961559$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Rekavandi, Aref Miri</creatorcontrib><creatorcontrib>Seghouane, Abd-Krim</creatorcontrib><creatorcontrib>Evans, Robin J.</creatorcontrib><title>Robust Subspace Detectors Based on α-Divergence With Application to Detection in Imaging</title><title>IEEE transactions on image processing</title><addtitle>TIP</addtitle><addtitle>IEEE Trans Image Process</addtitle><description><![CDATA[Robust variants of Wald, Rao and likelihood ratio (LR) tests for the detection of a signal subspace in a signal interference subspace corrupted by contaminated Gaussian noise are proposed in this paper. They are derived using the <inline-formula> <tex-math notation="LaTeX">\alpha - </tex-math></inline-formula>divergence, and the trade-off between the robustness and the power (the probability of detection) of the tests is adjustable using a single hyperparameter <inline-formula> <tex-math notation="LaTeX">\alpha </tex-math></inline-formula>. It is shown that when <inline-formula> <tex-math notation="LaTeX">\alpha \rightarrow 1 </tex-math></inline-formula>, these tests are equivalent to their well known classical counterparts. For example the robust LR test coincides with the LR test or the matched subspace detector (MSD). Asymptotic results are provided to support the proposed tests and robustness to outliers is obtained using values of <inline-formula> <tex-math notation="LaTeX">\alpha < 1 </tex-math></inline-formula>. Numerical experiments illustrating the performance of these tests on simulated, real functional magnetic resonance imaging (fMRI), hyperspectral and synthetic aperture radar (SAR) data are also presented.]]></description><subject><italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α -divergence</subject><subject>Detectors</subject><subject>Gaussian noise</subject><subject>Light rail systems</subject><subject>Likelihood ratio</subject><subject>likelihood ratio test</subject><subject>Magnetic resonance imaging</subject><subject>Maximum likelihood estimation</subject><subject>Outliers (statistics)</subject><subject>Pollution measurement</subject><subject>Random noise</subject><subject>Rao test</subject><subject>Robust detection</subject><subject>Robustness</subject><subject>Robustness (mathematics)</subject><subject>subspace detectors</subject><subject>Subspaces</subject><subject>Synthetic aperture radar</subject><subject>Uncertainty</subject><subject>Wald test</subject><issn>1057-7149</issn><issn>1941-0042</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkEtLxDAQx4Movu-CIAUvXrpmkvSR4_peWFB8IJ5Kkk7XSLetTSv4sfwifiZTtnrwMpkwv_8w_Ag5ADoBoPL0cXY3YZTBhNMkAS7XyDZIASGlgq37nkZJmICQW2THuTdKQUQQb5ItzmUMUSS3yct9rXvXBQ-9do0yGFxgh6arWxecKYd5UFfB91d4YT-wXWDlgWfbvQbTpimtUZ31464eQ8PHVsFsqRa2WuyRjUKVDvfHd5c8XV0-nt-E89vr2fl0Hhouki5MtTaFAsU4oxFVAlSuDce4kJxqlEmsgenYSMSC5WnBOIBOtaSpySOVAPJdcrLa27T1e4-uy5bWGSxLVWHdu4xFTPDYV-rR43_oW923lb9uoFIpOE_BU3RFmbZ2rsUia1q7VO1nBjQbtGdeezZoz0btPnI0Lu71EvO_wK9nDxyuAIuIf2MpWCxEzH8ABoaGaw</recordid><startdate>20210101</startdate><enddate>20210101</enddate><creator>Rekavandi, Aref Miri</creator><creator>Seghouane, Abd-Krim</creator><creator>Evans, Robin J.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0001-9542-759X</orcidid><orcidid>https://orcid.org/0000-0003-4619-734X</orcidid></search><sort><creationdate>20210101</creationdate><title>Robust Subspace Detectors Based on α-Divergence With Application to Detection in Imaging</title><author>Rekavandi, Aref Miri ; Seghouane, Abd-Krim ; Evans, Robin J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c347t-8bbcfa1a232050a41adbc3e6f930be976b12b6c9eef2d8f2311b8b908cd5a71e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic><italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α -divergence</topic><topic>Detectors</topic><topic>Gaussian noise</topic><topic>Light rail systems</topic><topic>Likelihood ratio</topic><topic>likelihood ratio test</topic><topic>Magnetic resonance imaging</topic><topic>Maximum likelihood estimation</topic><topic>Outliers (statistics)</topic><topic>Pollution measurement</topic><topic>Random noise</topic><topic>Rao test</topic><topic>Robust detection</topic><topic>Robustness</topic><topic>Robustness (mathematics)</topic><topic>subspace detectors</topic><topic>Subspaces</topic><topic>Synthetic aperture radar</topic><topic>Uncertainty</topic><topic>Wald test</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rekavandi, Aref Miri</creatorcontrib><creatorcontrib>Seghouane, Abd-Krim</creatorcontrib><creatorcontrib>Evans, Robin J.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</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>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>Rekavandi, Aref Miri</au><au>Seghouane, Abd-Krim</au><au>Evans, Robin J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Robust Subspace Detectors Based on α-Divergence With Application to Detection in Imaging</atitle><jtitle>IEEE transactions on image processing</jtitle><stitle>TIP</stitle><addtitle>IEEE Trans Image Process</addtitle><date>2021-01-01</date><risdate>2021</risdate><volume>30</volume><spage>5017</spage><epage>5031</epage><pages>5017-5031</pages><issn>1057-7149</issn><eissn>1941-0042</eissn><coden>IIPRE4</coden><abstract><![CDATA[Robust variants of Wald, Rao and likelihood ratio (LR) tests for the detection of a signal subspace in a signal interference subspace corrupted by contaminated Gaussian noise are proposed in this paper. They are derived using the <inline-formula> <tex-math notation="LaTeX">\alpha - </tex-math></inline-formula>divergence, and the trade-off between the robustness and the power (the probability of detection) of the tests is adjustable using a single hyperparameter <inline-formula> <tex-math notation="LaTeX">\alpha </tex-math></inline-formula>. It is shown that when <inline-formula> <tex-math notation="LaTeX">\alpha \rightarrow 1 </tex-math></inline-formula>, these tests are equivalent to their well known classical counterparts. For example the robust LR test coincides with the LR test or the matched subspace detector (MSD). Asymptotic results are provided to support the proposed tests and robustness to outliers is obtained using values of <inline-formula> <tex-math notation="LaTeX">\alpha < 1 </tex-math></inline-formula>. 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| subjects | <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α -divergence Detectors Gaussian noise Light rail systems Likelihood ratio likelihood ratio test Magnetic resonance imaging Maximum likelihood estimation Outliers (statistics) Pollution measurement Random noise Rao test Robust detection Robustness Robustness (mathematics) subspace detectors Subspaces Synthetic aperture radar Uncertainty Wald test |
| title | Robust Subspace Detectors Based on α-Divergence With Application to Detection in Imaging |
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