The University of Montana
Department of Mathematical Sciences

Technical report #24/2009

A Computational Framework for Total Variation-Regularized Positron Emission Tomography

Johnathan M. Bardsley and John Goldes

Abstract

In positron emission tomography, image data corresponds to measurements of emitted photons from a radioactive tracer in the subject. Such count data is typically modeled using a Poisson random variable, leading to the use of the negative-log Poisson likelihood fit-to-data function. Regularization is needed, however, in order to guarantee reconstructions with minimal artifacts. Given that tracer densities are primarily smoothly varying, but also contain sharp jumps (or edges), total variation regularization is a natural choice. However, the resulting computational problem is quite challenging. In this paper, we present a efficient computational method for this problem. We also introduce three regularization parameter choice methods for use on total variation-regularized negative-log Poisson likelihood problems, which to our knowledge, have not been presented elsewhere. We test the computational and regularization parameter selection methods on synthetic data.

Keywords: total variation, positron emission tomography, inverse problems, and statistical imaging

MSC numbers: 65J22, 65K10, and 65F22

Download Technical Report: Pdf (167 KB)