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>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Grantor dc:publisher

University of Montana

Year

2008

Author dc:creator

• Laobeul, N'Djekornom Dara

• Ill-Posed Poisson Imaging Problems
• Mathematical Theory
• Negative Poisson Likelihood

Repository record dc:identifier

https://scholarworks.umt.edu/etd/810

OAI identifier oai:identifier

oai:scholarworks.umt.edu:etd-1829