Poisson intensity estimation for tomographic data using a wavelet shrinkage approach
We consider a two-dimensional (2-D) problem of positron-emission tomography (PET) where the random mechanism of the generation of the tomographic data is modeled by Poisson processes. The goal is to estimate the intensity function which corresponds to emission density. Using the wavelet-vaguelette d...
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| Veröffentlicht in: | IEEE transactions on information theory 2002-10, Vol.48 (10), p.2794-2802 |
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| container_title | IEEE transactions on information theory |
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| creator | Cavalier, L. Ja-Yong Koo |
| description | We consider a two-dimensional (2-D) problem of positron-emission tomography (PET) where the random mechanism of the generation of the tomographic data is modeled by Poisson processes. The goal is to estimate the intensity function which corresponds to emission density. Using the wavelet-vaguelette decomposition (WVD), we propose an estimator based on thresholding of empirical vaguelette coefficients which attains the minimax rates of convergence on Besov function classes. Furthermore, we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term. |
| doi_str_mv | 10.1109/TIT.2002.802632 |
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The goal is to estimate the intensity function which corresponds to emission density. Using the wavelet-vaguelette decomposition (WVD), we propose an estimator based on thresholding of empirical vaguelette coefficients which attains the minimax rates of convergence on Besov function classes. Furthermore, we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2002.802632</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Adaptive estimation ; Adaptive systems ; Convergence ; Convergence of numerical methods ; Data reduction ; Density ; Emission ; Estimating techniques ; Estimators ; Inverse problems ; Linear programming ; Mathematical models ; Minimax methods ; Minimax technique ; Nonlinear programming ; Optimal systems ; Optimization ; Poisson distribution ; Positron emission tomography ; Random processes ; Stochastic processes ; Tomography ; Wavelet transforms</subject><ispartof>IEEE transactions on information theory, 2002-10, Vol.48 (10), p.2794-2802</ispartof><rights>Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Oct 2002</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c380t-cd4d254602fbce1e7b428702c2c82e57c6267657bc7674dbbffdbe3b09df6e733</citedby><cites>FETCH-LOGICAL-c380t-cd4d254602fbce1e7b428702c2c82e57c6267657bc7674dbbffdbe3b09df6e733</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/1035132$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27915,27916,54749</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/1035132$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Cavalier, L.</creatorcontrib><creatorcontrib>Ja-Yong Koo</creatorcontrib><title>Poisson intensity estimation for tomographic data using a wavelet shrinkage approach</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>We consider a two-dimensional (2-D) problem of positron-emission tomography (PET) where the random mechanism of the generation of the tomographic data is modeled by Poisson processes. 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Furthermore, we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term.</description><subject>Adaptive estimation</subject><subject>Adaptive systems</subject><subject>Convergence</subject><subject>Convergence of numerical methods</subject><subject>Data reduction</subject><subject>Density</subject><subject>Emission</subject><subject>Estimating techniques</subject><subject>Estimators</subject><subject>Inverse problems</subject><subject>Linear programming</subject><subject>Mathematical models</subject><subject>Minimax methods</subject><subject>Minimax technique</subject><subject>Nonlinear programming</subject><subject>Optimal systems</subject><subject>Optimization</subject><subject>Poisson distribution</subject><subject>Positron emission tomography</subject><subject>Random processes</subject><subject>Stochastic processes</subject><subject>Tomography</subject><subject>Wavelet transforms</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqFkTtPwzAQxy0EEqUwM7BYDDCl9TNORlTxqFQJhjJbjnNpXdq42Amo3x5XZUAMMJ3u7nfPP0KXlIwoJeV4Pp2PGCFsVBCWc3aEBlRKlZW5FMdoQAgtslKI4hSdxbhKrpCUDdD8xbsYfYtd20EbXbfDEDu3MZ1LwcYH3PmNXwSzXTqLa9MZ3EfXLrDBn-YD1tDhuAyufTMLwGa7Dd7Y5Tk6acw6wsW3HaLXh_v55CmbPT9OJ3ezzPKCdJmtRc2kyAlrKgsUVCVYoQizzBYMpLI5y1UuVWVVrkRdVU1TV8ArUtZNDorzIbo99E1j3_u0t964aGG9Ni34PuqSqFIoxVQib_4kWSEll0z8D1JJKOf7jte_wJXvQ5vO1bSURRpKWILGB8gGH2OARm9D-m3YaUr0XjWdVNN71fRBtVRxdahwAPCD5pKm7BfVc5Nz</recordid><startdate>20021001</startdate><enddate>20021001</enddate><creator>Cavalier, L.</creator><creator>Ja-Yong Koo</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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The goal is to estimate the intensity function which corresponds to emission density. Using the wavelet-vaguelette decomposition (WVD), we propose an estimator based on thresholding of empirical vaguelette coefficients which attains the minimax rates of convergence on Besov function classes. Furthermore, we construct an adaptive estimator which attains the optimal rate of convergence up to a logarithmic term.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TIT.2002.802632</doi><tpages>9</tpages></addata></record> |
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| subjects | Adaptive estimation Adaptive systems Convergence Convergence of numerical methods Data reduction Density Emission Estimating techniques Estimators Inverse problems Linear programming Mathematical models Minimax methods Minimax technique Nonlinear programming Optimal systems Optimization Poisson distribution Positron emission tomography Random processes Stochastic processes Tomography Wavelet transforms |
| title | Poisson intensity estimation for tomographic data using a wavelet shrinkage approach |
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