Noise2Score: Tweedie’s Approach to Self-Supervised Image Denoising without Clean Images
Authors: Kwanyoung Kim, Jong Chul Ye

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 loglikelihood). 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.