Properties of Noise in Positron Emission Tomography Images Reconstructed with Filtered-Backprojection and Row-Action Maximum Likelihood Algorithm

Noise levels observed in positron emission tomography (PET) images complicate their geometric interpretation. Post-processing techniques aimed at noise reduction may be employed to overcome this problem. The detailed characteristics of the noise affecting PET images are, however, often not well known. Typically, it is assumed that overall the noise may be characterized as Gaussian. Other PET-imaging-related studies have been specifically aimed at the reduction of noise represented by a Poisson or mixed Poisson + Gaussian model. The effectiveness of any approach to noise reduction greatly depends on a proper quantification of the characteristics of the noise present. This work examines the statistical properties of noise in PET images acquired with a GEMINI PET/CT scanner. Noise measurements have been performed with a cylindrical phantom injected with ¹¹C and well mixed to provide a uniform activity distribution. Images were acquired using standard clinical protocols and reconstructed with filtered-backprojection (FBP) and row-action maximum likelihood algorithm (RAMLA). Statistical properties of the acquired data were evaluated and compared to five noise models (Poisson, normal, negative binomial, log-normal, and gamma). Histograms of the experimental data were used to calculate cumulative distribution functions and produce maximum likelihood estimates for the parameters of the model distributions. Results obtained confirm the poor representation of both RAMLA- and FBP-reconstructed PET data by the Poisson distribution. We demonstrate that the noise in RAMLA-reconstructed PET images is very well characterized by gamma distribution followed closely by normal distribution, while FBP produces comparable conformity with both normal and gamma statistics.