A new bayesian Poisson denoising algorithm based on nonlocal means and stochastic distances

•A novel, mathematically formal and computationally efficient bayesian approach to Poisson denoising.•It is based on the conjugacy of the Poisson and Gamma distributions, avoiding high cost procedures.•The method is applied to denoising low-dose CT sinograms, using a non-local means filtering algorithm, replacing the euclidean distances by stochastic distances for the Gamma distribution.•The proposed algorithm is competitive with several important algorithms of the literature. [Display omitted] Poisson noise is the main cause of degradation of many imaging modalities. However, many of the proposed methods for reducing noise in images lack a formal approach. Our work develops a new, general, formal and computationally efficient bayesian Poisson denoising algorithm, based on the Nonlocal Means framework and replacing the euclidean distance by stochastic distances, which are more appropriate for the denoising problem. It takes advantage of the conjugacy of Poisson and gamma distributions to obtain its computational efficiency. When dealing with low dose CT images, the algorithm operates on the sinogram, modeling the rates of the Poisson noise by the Gamma distribution. Based on the Bayesian formulation and the conjugacy property, the likelihood follows the Poisson distribution, while the a posteriori distribution is also described by the Gamma distribution. The derived algorithm is applied to simulated and real low-dose CT images and compared to several algorithms proposed in the literature, with competitive results.