Image reconstruction of PET images using denoised data

In this paper, we propose a reconstruction methodology where PET data are post-processed using Poisson denoising algorithms developed by Timmermann and Nowak (1999). The denoising algorithms, which follow from a Bayesian framework and multiscale signal representation, compute minimum mean square error estimates of the unknown means of independent Poisson random variables from their observations. Timmermann and Nowak estimated certain parameters needed by their algorithms using the method of moments and observed data. Instead, we estimate these parameters more accurately using a maximum likelihood method and off-line training procedure. We demonstrate the utility of the proposed image reconstruction methodology by applying it to synthetic data and real positron emission tomography data.