Concurrent Segmentation and Estimation of Transmission Images for Attenuation Correction in Positron Emission Tomography

When transmission images are obtained using conventional reconstruction methods in stand alone PET scanners, such as standard clinical PET, microPET, and dedicated brain scanners, the results may be noisy and/or inaccurate. For example, the popular penalized maximum-likelihood method effectively reduces noise, but it does not address the bias problem that results from the incorporation of a penalty function and contamination from emission data due to patient activity. In this paper, we present an algorithm that simultaneously reconstructs transmission images and performs a ldquosoftrdquo segmentation of voxels into the classes: air, patient bed, lung, soft-tissue, and bone. It is through the segmentation step that the algorithm, which we refer to as the concurrent segmentation and estimation (CSE) algorithm, provides a means for incorporating accurate attenuation coefficients. The CSE algorithm is obtained by applying an expectation-maximization like formulation to a certain maximum a posterior objective function. This formulation enables us to show that the CSE algorithm monotonically increases the objective function. In experiments using real phantom and synthetic data, the CSE images produced attenuation correction factors and emission images that were more accurate than those obtained using a popular segmentation based attenuation correction method, and the penalized maximum likelihood and filtered backprojection methods.