Adaptive nonlinear probabilistic filter for Positron Emission Tomography

Radiologists face difficulties when reading and interpreting Positron Emission Tomography (PET) images because of the high noise level in the raw-projection data (i.e. the sinogram). The later may lead to erroneous diagnoses. Aiming at finding a suitable denoising technique for PET images, in our first work, we investigated filtering the sinogram with a constraint curvature motion filter where we computed the edge stopping function in terms of edge probability under a marginal prior on the noise free gradient. In this paper, we show that the Chi-square is the appropriate prior for finding the edge probability in the sinogram noise-free gradient. Since the sinogram noise is uncorrelated and follows a Poisson distribution, we then propose an adaptive probabilistic diffusivity function where the edge probability is computed at each pixel. We demonstrate quantitatively and qualitatively through simulations that the performance of the proposed method substantially surpasses that of state-of-art methods, both visually and in terms of statistical measures.