Simultaneous Estimation of PET Attenuation and Activity Images with Divided Difference Filters

For quantitative image reconstruction in positron emission tomography attenuation correction is necessary. A common technique used for attenuation correction is based on patient-specific attenuation maps reconstructed from transmission data acquired with external sources. However, the transmission process increases measurement time, costs and radiation exposure, and generates misregistration errors due to patient motion. In this paper, we propose a framework for simultaneous reconstruction of activity distribution together with the attenuation map from emission data alone. The estimation process is accomplished by solving a nonlinear stationary state space model with a divided difference filter. A Zubal digital thorax phantom data is used to demonstrate the benefits of such a reconstruction.