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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Laobeul, N'Djekornom Dara"],"institution":"University of Montana","degree_name":"Doctor of Philosophy (PhD)","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-01-01T08:00:00Z","date_published":"2008-01-01T08:00:00Z","updated_at":"2026-07-24T03:13:53Z","subjects":["Ill-Posed Poisson Imaging Problems","Mathematical Theory","Negative Poisson Likelihood"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.umt.edu/etd/810","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Laobeul, N'Djekornom Dara"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["University of Montana"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Ill-Posed Poisson Imaging Problems","Mathematical Theory","Negative Poisson Likelihood"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.umt.edu/etd/810"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["REGULARIZATION METHODS FOR ILL-POSED POISSON IMAGING"]}]}],"canonical_facts":{"dc:creator":["Laobeul, N'Djekornom Dara"],"dc:description.abstract":["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.
"],"dc:identifier":["https://scholarworks.umt.edu/etd/810"],"dc:publisher":["University of Montana"],"dc:subject":["Ill-Posed Poisson Imaging Problems","Mathematical Theory","Negative Poisson Likelihood"],"dc:title":["REGULARIZATION METHODS FOR ILL-POSED POISSON IMAGING"],"dc:type":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:13:53Z"}