Recorrupted-to-Recorrupted (R2R) has emerged as a methodology for training deep networks for image restoration in a self-supervised manner from noisy measurement data alone, demonstrating equivalence in expectation to the supervised squared loss in the case of Gaussian noise. However, its effectiveness with non-Gaussian noise remains unexplored. In this paper, we propose Generalized R2R (GR2R), extending the R2R framework to handle a broader class of noise distribution as additive noise like log-Rayleigh and address the natural exponential family including Poisson and Gamma noise distributions, which play a key role in many applications including low-photon imaging and synthetic aperture radar. We show that the GR2R loss is an unbiased estimator of the supervised loss and that the popular Stein's unbiased risk estimator can be seen as a special case. A series of experiments with Gaussian, Poisson, and Gamma noise validate GR2R's performance, showing its effectiveness compared to other self-supervised methods.

翻译：再损坏至再损坏（R2R）已成为一种仅从含噪测量数据中以自监督方式训练深度网络进行图像恢复的方法，在高斯噪声情形下，其期望已证明与监督平方损失等价。然而，其在非高斯噪声下的有效性尚未得到探索。本文提出广义化R2R（GR2R），将R2R框架扩展至处理更广泛的噪声分布类别，如作为加性噪声的对数瑞利噪声，并处理包括泊松与伽马噪声分布在内的自然指数族噪声，这些噪声在低光子成像与合成孔径雷达等诸多应用中扮演关键角色。我们证明GR2R损失是监督损失的无偏估计量，且流行的Stein无偏风险估计量可视为其特例。一系列针对高斯、泊松与伽马噪声的实验验证了GR2R的性能，表明其相较于其他自监督方法的有效性。