Fisher Information as a Metric of Locally Optimal Processing and Stochastic Resonance
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Auteurs : Fabing Duan [République populaire de Chine] ; François Chapeau-Blondeau [France] ; Derek Abbott [Australie]Source :
- PLoS ONE [ 1932-6203 ] ; 2012.
Abstract
The origins of Fisher information are in its use as a performance measure for parametric estimation. We augment this and show that the Fisher information can characterize the performance in several other significant signal processing operations. For processing of a weak signal in additive white noise, we demonstrate that the Fisher information determines (i) the maximum output signal-to-noise ratio for a periodic signal; (ii) the optimum asymptotic efficacy for signal detection; (iii) the best cross-correlation coefficient for signal transmission; and (iv) the minimum mean square error of an unbiased estimator. This unifying picture, via inequalities on the Fisher information, is used to establish conditions where improvement by noise through stochastic resonance is feasible or not.
Url:
DOI: 10.1371/journal.pone.0034282
PubMed: 22493686
PubMed Central: 3320899
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Fisher Information as a Metric of Locally Optimal Processing and Stochastic Resonance</title><author><name sortKey="Duan, Fabing" sort="Duan, Fabing" uniqKey="Duan F" first="Fabing" last="Duan">Fabing Duan</name><affiliation wicri:level="1"><nlm:aff id="aff1"><addr-line>College of Automation Engineering, Qingdao University, Qingdao, People's Republic of China</addr-line></nlm:aff><country xml:lang="fr">République populaire de Chine</country><wicri:regionArea>College of Automation Engineering, Qingdao University, Qingdao</wicri:regionArea></affiliation></author><author><name sortKey="Chapeau Blondeau, Francois" sort="Chapeau Blondeau, Francois" uniqKey="Chapeau Blondeau F" first="François" last="Chapeau-Blondeau">François Chapeau-Blondeau</name><affiliation wicri:level="1"><nlm:aff id="aff2"><addr-line>Laboratoire d'Ingénierie des Systèmes Automatisés (LISA), Université d'Angers, Angers, France</addr-line></nlm:aff><country xml:lang="fr">France</country><wicri:regionArea>Laboratoire d'Ingénierie des Systèmes Automatisés (LISA), Université d'Angers, Angers</wicri:regionArea></affiliation></author><author><name sortKey="Abbott, Derek" sort="Abbott, Derek" uniqKey="Abbott D" first="Derek" last="Abbott">Derek Abbott</name><affiliation wicri:level="1"><nlm:aff id="aff3"><addr-line>Centre for Biomedical Engineering (CBME) and School of Electrical & Electronic Engineering, The University of Adelaide, Adelaide, Southern Australia, Australia</addr-line></nlm:aff><country xml:lang="fr">Australie</country><wicri:regionArea>Centre for Biomedical Engineering (CBME) and School of Electrical & Electronic Engineering, The University of Adelaide, Adelaide, Southern Australia</wicri:regionArea></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">22493686</idno><idno type="pmc">3320899</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3320899</idno><idno type="RBID">PMC:3320899</idno><idno type="doi">10.1371/journal.pone.0034282</idno><date when="2012">2012</date><idno type="wicri:Area/Pmc/Corpus">002A07</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">002A07</idno><idno type="wicri:Area/Pmc/Curation">002857</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Curation">002857</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Fisher Information as a Metric of Locally Optimal Processing and Stochastic Resonance</title><author><name sortKey="Duan, Fabing" sort="Duan, Fabing" uniqKey="Duan F" first="Fabing" last="Duan">Fabing Duan</name><affiliation wicri:level="1"><nlm:aff id="aff1"><addr-line>College of Automation Engineering, Qingdao University, Qingdao, People's Republic of China</addr-line></nlm:aff><country xml:lang="fr">République populaire de Chine</country><wicri:regionArea>College of Automation Engineering, Qingdao University, Qingdao</wicri:regionArea></affiliation></author><author><name sortKey="Chapeau Blondeau, Francois" sort="Chapeau Blondeau, Francois" uniqKey="Chapeau Blondeau F" first="François" last="Chapeau-Blondeau">François Chapeau-Blondeau</name><affiliation wicri:level="1"><nlm:aff id="aff2"><addr-line>Laboratoire d'Ingénierie des Systèmes Automatisés (LISA), Université d'Angers, Angers, France</addr-line></nlm:aff><country xml:lang="fr">France</country><wicri:regionArea>Laboratoire d'Ingénierie des Systèmes Automatisés (LISA), Université d'Angers, Angers</wicri:regionArea></affiliation></author><author><name sortKey="Abbott, Derek" sort="Abbott, Derek" uniqKey="Abbott D" first="Derek" last="Abbott">Derek Abbott</name><affiliation wicri:level="1"><nlm:aff id="aff3"><addr-line>Centre for Biomedical Engineering (CBME) and School of Electrical & Electronic Engineering, The University of Adelaide, Adelaide, Southern Australia, Australia</addr-line></nlm:aff><country xml:lang="fr">Australie</country><wicri:regionArea>Centre for Biomedical Engineering (CBME) and School of Electrical & Electronic Engineering, The University of Adelaide, Adelaide, Southern Australia</wicri:regionArea></affiliation></author></analytic><series><title level="j">PLoS ONE</title><idno type="eISSN">1932-6203</idno><imprint><date when="2012">2012</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>The origins of Fisher information are in its use as a performance measure for parametric estimation. We augment this and show that the Fisher information can characterize the performance in several other significant signal processing operations. For processing of a weak signal in additive white noise, we demonstrate that the Fisher information determines (i) the maximum output signal-to-noise ratio for a periodic signal; (ii) the optimum asymptotic efficacy for signal detection; (iii) the best cross-correlation coefficient for signal transmission; and (iv) the minimum mean square error of an unbiased estimator. This unifying picture, via inequalities on the Fisher information, is used to establish conditions where improvement by noise through stochastic resonance is feasible or not.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Cover, Tm" uniqKey="Cover T">TM Cover</name></author><author><name sortKey="Thomas, Ja" uniqKey="Thomas J">JA Thomas</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kay, S" uniqKey="Kay S">S Kay</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Capon, J" uniqKey="Capon J">J Capon</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Poor, Hv" uniqKey="Poor H">HV Poor</name></author><author><name sortKey="Thomas, Jb" uniqKey="Thomas J">JB Thomas</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lu, Nh" uniqKey="Lu N">NH Lu</name></author><author><name sortKey="Eisenstein, B" 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article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">PLoS One</journal-id><journal-id journal-id-type="iso-abbrev">PLoS ONE</journal-id><journal-id journal-id-type="publisher-id">plos</journal-id><journal-id journal-id-type="pmc">plosone</journal-id><journal-title-group><journal-title>PLoS ONE</journal-title></journal-title-group><issn pub-type="epub">1932-6203</issn><publisher><publisher-name>Public Library of Science</publisher-name><publisher-loc>San Francisco, USA</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">22493686</article-id><article-id pub-id-type="pmc">3320899</article-id><article-id pub-id-type="publisher-id">PONE-D-12-03221</article-id><article-id pub-id-type="doi">10.1371/journal.pone.0034282</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Engineering</subject><subj-group><subject>Signal Processing</subject></subj-group></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Mathematics</subject><subj-group><subject>Probability Theory</subject></subj-group></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Physics</subject><subj-group><subject>Interdisciplinary Physics</subject></subj-group></subj-group></article-categories><title-group><article-title>Fisher Information as a Metric of Locally Optimal Processing and Stochastic Resonance</article-title><alt-title alt-title-type="running-head">Fisher Information for Stochastic Resonance</alt-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Duan</surname><given-names>Fabing</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib><contrib contrib-type="author"><name><surname>Chapeau-Blondeau</surname><given-names>François</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Abbott</surname><given-names>Derek</given-names></name><xref ref-type="aff" rid="aff3"><sup>3</sup></xref></contrib></contrib-group><aff id="aff1"><label>1</label><addr-line>College of Automation Engineering, Qingdao University, Qingdao, People's Republic of China</addr-line></aff><aff id="aff2"><label>2</label><addr-line>Laboratoire d'Ingénierie des Systèmes Automatisés (LISA), Université d'Angers, Angers, France</addr-line></aff><aff id="aff3"><label>3</label><addr-line>Centre for Biomedical Engineering (CBME) and School of Electrical & Electronic Engineering, The University of Adelaide, Adelaide, Southern Australia, Australia</addr-line></aff><contrib-group><contrib contrib-type="editor"><name><surname>Perc</surname><given-names>Matjaz</given-names></name><role>Editor</role><xref ref-type="aff" rid="edit1"></xref></contrib></contrib-group><aff id="edit1">University of Maribor, Slovenia</aff><author-notes><corresp id="cor1">* E-mail: <email>fabing.duan@gmail.com</email></corresp><fn fn-type="con"><p>Conceived and designed the experiments: FD. Performed the experiments: FD FCB DA. Analyzed the data: FD FCB DA. Contributed reagents/materials/analysis tools: FCB DA. Wrote the paper: FD. Proofreading: FCB DA.</p></fn></author-notes><pub-date pub-type="collection"><year>2012</year></pub-date><pub-date pub-type="epub"><day>6</day><month>4</month><year>2012</year></pub-date><volume>7</volume><issue>4</issue><elocation-id>e34282</elocation-id><history><date date-type="received"><day>1</day><month>2</month><year>2012</year></date><date date-type="accepted"><day>25</day><month>2</month><year>2012</year></date></history><permissions><copyright-statement>Duan et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</copyright-statement><copyright-year>2012</copyright-year></permissions><abstract><p>The origins of Fisher information are in its use as a performance measure for parametric estimation. We augment this and show that the Fisher information can characterize the performance in several other significant signal processing operations. For processing of a weak signal in additive white noise, we demonstrate that the Fisher information determines (i) the maximum output signal-to-noise ratio for a periodic signal; (ii) the optimum asymptotic efficacy for signal detection; (iii) the best cross-correlation coefficient for signal transmission; and (iv) the minimum mean square error of an unbiased estimator. This unifying picture, via inequalities on the Fisher information, is used to establish conditions where improvement by noise through stochastic resonance is feasible or not.</p></abstract><counts><page-count count="6"></page-count></counts></article-meta></front></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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