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REGULARIZATION METHODS FOR ILL-POSED POISSON IMAGING

<P>The noise contained in images collected by a charge coupled device (CCD) camera is predominantly of Poisson type. This motivates the use of the negative logarithm of the Poisson likelihood in place of the ubiquitous least squares t-to-data. However, if the underlying mathematical model is assumed to have the form z = Au, where A is a linear, compact operator, the problem of minimizing the negative log-Poisson likelihood function is ill-posed, and hence some form of regularization is required. In this work, it involves solving a variational problem of the form u def = arg min u0 `(Au; z) + J(u); where ` is the negative-log of a Poisson likelihood functional, and J is a regularization functional. The main result of this thesis is a theoretical analysis of this variational problem for four dierent regularization functionals. In addition, this work presents an ecient computational method for its solution, and the demonstration of the eectiveness of this approach in practice by applying the algorithm to simulated astronomical imaging data corrupted by the CCD camera noise model mentioned above.</P>

Identiferoai:union.ndltd.org:MONTANA/oai:etd.lib.umt.edu:etd-12092008-133704
Date15 January 2009
CreatorsLaobeul, N'Djekornom Dara
ContributorsJesse Johnson, Brian Steele, Leonid Kalachev, Thomas Tonev, Johnathan Bardsley
PublisherThe University of Montana
Source SetsUniversity of Montana Missoula
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.umt.edu/theses/available/etd-12092008-133704/
Rightsunrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Montana or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.

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