Approximate Bayesian computation, stochastic algorithms and non-local means for complex noise models

In this paper, we present a stochastic NL-means-based de-noising algorithm for generalized non-parametric noise models. First, we provide a statistical interpretation to current patch-based neighborhood filters and justify the Bayesian inference that needs to explicitly accounts for discrepancies between the model and the data. Furthermore, we investigate the Approximate Bayesian Computation (ABC) rejection method combined with density learning techniques for handling situations where the posterior is intractable or too prohibitive to calculate. We demonstrate our stochastic Gamma NL-means (SGNL) on real images corrupted by non-Gaussian noise.