State space approach for joint estimation of activity and attenuation map from PET emission sinograms

State space approach for joint estimation of activity and attenuation map from PET emission sinograms

Quantitative estimation of radioactivity map has important clinical implications for better diagnosis and understanding of cancers. Although attenuation map and activity map are usually treated sequentially, they can obviously benefit a great deal when the transmission data is missing. In this paper, we propose a novel scheme of simultaneously solving for attenuation map and activity distribution from emission sinograms. Our strategy combines the measurement model of PET, and the attenuation parameters are treated as random variables with known prior statistics. After the conversion to state space representation, the extended Kalman filtering procedures are adopted to linearize the equations and to provide the joint estimates in an approximate optimal sense. Experiments have been performed on both synthetic data to illustrate its abilities and benefits