Transmission tomography reconstruction using compound Gauss-Markov random fields and ordered subsets

Emission tomography images are degraded due to the presence of noise and several physical factors, like attenuation and scattering. To remove the attenuation effect from the emission tomography reconstruction, attenuation correction factors (ACFs) are used. These ACFs are obtained from a transmission scan and it is well known that they are homogeneous within each tissue and present abrupt variations in the transition between tissues. In this paper we propose the use of compound Gauss Markov random fields (CGMRF) as prior distributions to model homogeneity within tissues and high variations between regions. In order to find the maximum a posteriori (MAP) estimate of the reconstructed image we propose a new iterative method, which is stochastic for the line process and deterministic for the reconstruction. We apply the ordered subsets (OS) principle to accelerate the image reconstruction. The proposed method is tested and compared with other reconstruction methods.