The University of Montana
Department of Mathematical Sciences

Technical report #15/2009

Regularization Parameter Selection Methods for Ill-Posed Poisson Maximum Likelihood Estimation

Johnathan M. Bardsley and John Goldes

Abstract

In image processing applications, image intensity is often measured via the counting of incident photons emitted by the object of interest. In such cases, image data-noise is accurately modeled by a Poisson distribution. This motivates the use of Poisson maximum likelihood estimation for image reconstruction. However, when the underlying model equation is ill-posed, regularization is needed. Regularized Poisson likelihood estimation has been studied extensively by the authors, though a problem of high importance remains: the choice of the regularization parameter. We will present three statistically motivated methods for choosing the regularization parameter, and numerical examples will be presented to illustrate their effectiveness.

Keywords: regularization parameter selection methods, Poisson maximum likelihood estimation, ill-posed problems, image reconstruction.

MSC numbers: 15A29, 65F22, 94A08

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