Poisson denoising under a Bayesian nonlocal approach using geodesic distances with low-dose CT applications

Abstract Poisson noise tends to be the primary source of image degradation in several applications. When reducing the exposure time, the image may be severely degraded by noise. One of the strategies is to use adaptations of Non-Local Means for filtering. The NLM algorithm filters an image using a non-local average weighted by a function of the Euclidean distance between two patches of the image. Since geodesic distances induce a metric for the dissimilarity between two distributions, they can be used to compare two patches of an image. This paper alters the NLM algorithm to filter Poisson noise by changing the distance metric with a geodesic one that is more representative of this type of noise, adopting a general, and computationally efficient Bayesian approach. We evaluate the proposed method in the context of low-dose sinogram denoising. Among the geodesic distances evaluated, we found a closed solution for the Shannon entropy for Gamma distributions. Comparisons are made with other NLM strategies as well as state-of-the-art methods, achieving competitive results.