Uncertainty penalized weighted least squares framework for PET reconstruction under uncertain system models

In positron emission tomography (PET), an optimal estimate of the radio activity concentration is obtained from the measured emission data under some criteria. So far, all the well-known reconstruction algorithms require exact known system probability matrix a priori, where the quality of such system model largely determines the quality of the reconstructed images, especially for the least-squares strategies. In this paper, we propose an algorithm for PET reconstruction for the real world case where the PET system model is subject to uncertainties. The method is based on the formulation of PET reconstruction as a regularization problem and the image estimation is achieved with the aid of an uncertainty-weighted least squares framework. The performance of our work is evaluated using the Shepp-Logan simulated phantom data, where it yields significant improvement in image quality over the conventional least-squares reconstruction efforts.