Year of Award
2008
Document Type
Dissertation
Degree Type
Doctor of Philosophy (PhD)
Other Degree Name/Area of Focus
Mathematical Sciences
Department or School/College
Department of Mathematics
Committee Chair
Johnathan Bardsley
Commitee Members
Thomas Tonev, Leonid Kalachev, Brian Steele, Jesse Johnson
Keywords
Ill-Posed Poisson Imaging Problems, Mathematical Theory, Negative Poisson Likelihood
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.
Recommended Citation
Laobeul, N'Djekornom Dara, "REGULARIZATION METHODS FOR ILL-POSED POISSON IMAGING" (2008). Graduate Student Theses, Dissertations, & Professional Papers. 810.
https://scholarworks.umt.edu/etd/810
© Copyright 2008 N'Djekornom Dara Laobeul