Recently, there has been extensive research interest in training deep networks to denoise images without clean reference. However, the representative approaches such as Noise2Noise, Noise2Void, Stein's unbiased risk estimator (SURE), etc. seem to differ from one another and it is difficult to find the coherent mathematical structure. To address this, here we present a novel approach, called Noise2Score, which reveals a missing link in order to unite these seemingly different approaches. Specifically, we show that image denoising problems without clean images can be addressed by finding the mode of the posterior distribution and that the Tweedie's formula offers an explicit solution through the score function (i.e. the gradient of log likelihood). Our method then uses the recent finding that the score function can be stably estimated from the noisy images using the amortized residual denoising autoencoder, the method of which is closely related to Noise2Noise or Nose2Void. Our Noise2Score approach is so universal that the same network training can be used to remove noises from images that are corrupted by any exponential family distributions and noise parameters. Using extensive experiments with Gaussian, Poisson, and Gamma noises, we show that Noise2Score significantly outperforms the state-of-the-art self-supervised denoising methods in the benchmark data set such as (C)BSD68, Set12, and Kodak, etc.

本研究提出一种名为Noise2Score的新方法，通过发现后验分布的模式并使用梯度的得分函数来解决无干净参考图像的图像去噪问题，该方法可以处理任何指数族分布和噪声参数下受损图像的降噪，并在实验中表现出比现有方法更佳的性能。

Noise2Score：基于 Tweedie 的自监督图像去噪方法无需干净图像