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 Under such conditions, the variance stabilization transform (VST) is no longer applicable, so that the state-of-the-art algorithms which are proficient for the additive white Gaussian noise cannot be applied.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.

在本文中，我们针对泊松散粒噪声模型解决了在弱光条件下获得的图像去噪的问题。在这种情况下，方差稳定变换（VST）不再适用，因此无法应用精通加性高斯白噪声的最新算法。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. 我们还证明，当在指定的误差范围内估算oracle函数时，收敛性仍然有效。然后，我们通过对确定oracle权重的相似度函数进行统计估计来定义可实现的过滤器。通过证明相似性函数的估计值很有可能位于规定的误差范围内，来证明可实现滤波器的收敛性。实验表明，在弱光条件下，与最近的最新算法相比，该滤波器具有竞争优势。