Poisson Shot Noise Removal by an Oracular Non-Local Algorithm

In this paper, we address the problem of denoising images obtained under low-light conditions for the Poisson shot noise model. Under such conditions, the variance stabilization transform (VST) is no longer applicable, so that the state-of-the-art algorithms which are proficient for the additive white Gaussian noise cannot be applied. We first introduce an oracular non-local algorithm and prove its convergence with the optimal rate of convergence under a Hölder regularity assumption for the underlying image, when the search window size is suitably chosen. We also prove that the convergence remains valid when the oracle function is estimated within a prescribed error range. We then define a realizable filter by a statistical estimation of the similarity function which determines the oracle weight. The convergence of the realizable filter is justified by proving that the estimator of the similarity function lies in the prescribed error range with high probability. The experiments show that under low-light conditions the proposed filter is competitive compared with the recent state-of-the-art algorithms.