The University of Montana
Department of Mathematical Sciences

Technical report #11/2009

An Nonnegatively Constrained Iterative Method for Positron Emission Tomography

Johnathan M. Bardsley

Abstract

In positron emission tomography (PET), data is collected via the detection of photons emitted by a radioactive tracer within the subject. The noise in PET data is Poisson, and hence, it is typical to reconstruct the tracer density distribution via the computation of an approximate minimizer of the negative-log Poisson likelihood function. In this paper, we present an iterative method for the solution of the PET inverse problem. A weighted least squares approximation of the negative-log Poisson likelihood is used. The method is nonnegatively constrained and, due to the ill-conditioned nature of the PET inverse problem, requires a stopping rule for its iterations. We present a statistically motivated stopping rule based on the χ2-test. The approach is implemented on a synthetically generated example, and is shown to be effective.

Keywords: positron emission tomography, iterative methods, regularization, statistical methods.

AMS Subject Classification: 65J22, 65K10, 65F22

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