Regularization Methods for Ill-Posed Poisson Imaging Problems: An Introduction and Overview

Authors

N'djekornom Dara Laobeul, University of Montana

Document Type

Presentation Abstract

Presentation Date

4-24-2008

Abstract

In this talk, we discuss the following deblurring method: solve

u_∝ := arg min_u≥0 ℓ (Au;z) = ∝J(u)

where z is blurred, noisy data, A is a compact operator,ℓ is the negative-log of the Poisson likelihood function, α > 0 is the regularization parameter, and J is the regularization functional. We will discuss the notions of ill-posedness, regularization, and also how the choice of the functional J effects the properties of the deblurred image uα.

Lastly, we will present the computational technique used in practice to obtain uα and some numerical results with three different regularization functions.

Our goal will be to present the main ideas of our work in a way that is accessible to a broad audience.

Additional Details

Thursday, 24 April 2008
4:10 p.m. in 103
3:30 p.m. Refreshments in Math Lounge 109

Recommended Citation

Laobeul, N'djekornom Dara, "Regularization Methods for Ill-Posed Poisson Imaging Problems: An Introduction and Overview" (2008). Colloquia of the Department of Mathematical Sciences. 290.
https://scholarworks.umt.edu/mathcolloquia/290