REGULARIZATION PARAMETER SELECTION METHODS FOR ILL POSED POISSON IMAGING PROBLEMS

Author

John Goldes, The University of Montana

Year of Award

2010

Document Type

Dissertation

Degree Type

Doctor of Philosophy (PhD)

Degree Name

Mathematics

Other Degree Name/Area of Focus

Applied Mathematics

Department or School/College

Department of Mathematical Sciences

Committee Chair

John M. Bardsley

Commitee Members

Leonid Kalachev, Emily Stone, Jennifer Halfpap, Jesse Johnson

Abstract

A common problem in imaging science is to estimate some underlying true image given noisy measurements of image intensity. When image intensity is measured by the counting of incident photons emitted by the object of interest, the data-noise is accurately modeled by a Poisson distribution, which motivates the use of Poisson maximum likelihood estimation. When the underlying model equation is ill-posed, regularization must be employed. I will present a computational framework for solving such problems, including statistically motivated methods for choosing the regularization parameter. Numerical examples will be included.

Recommended Citation

Goldes, John, "REGULARIZATION PARAMETER SELECTION METHODS FOR ILL POSED POISSON IMAGING PROBLEMS" (2010). Graduate Student Theses, Dissertations, & Professional Papers. 811.
https://scholarworks.umt.edu/etd/811