The University of Montana
Department of Mathematical Sciences

Technical report #23/2010

A Nonnegatively Constrained Iterative Method with Statistically Based Stopping Rules for CT, PET, and SPECT Imaging

Johnatha M. Bardsley, Univ. of Montana

Abstract

In this paper, we extend a nonnegatively constrained iterative method and three stopping rules for its iterations to the medical imaging inverse problems of computed tomography (CT), positron emission tomography (PET), and single photon emission computed tomography (SPECT); the iterative method and stopping rules were introduced for use in astronomical imaging. The paper begins with a brief introduction to the CT, PET, and SPECT mathematical and statistical models. The iterative method and stopping rules are then presented. And finally, numerical experiments are presented to validate the methods.

Keywords: nonnegatively constrained iterative methods, inverse problems, statistical methods, medical imaging

MSC numbers: 65J22, 65K10, 65F22

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