Recorrupted-to-Noise: A Unifying Framework for Recorruption-Based Self-Supervised Denoising

Self-supervised learning has emerged as an effective paradigm for image denoising when clean ground-truth data are expensive or unavailable. Existing approaches often rely on restrictive assumptions regarding noise independence or distribution, limiting their applicability across imaging scenarios. In this paper, we introduce a Recorrupted-to-Noise (R2N) self-supervised denoising framework, which offers a unified theoretical interpretation of recorruption-based denoising methods. R2N recorrupts noisy observations and trains a network to predict the recorruption noise. The validity of R2N rests on conditional projective equivalence (CPE) between the observation noise and the recorruption noise, a weaker condition than those required by many existing self-supervised denoising methods. This condition supports a broad range of noise models, including general additive noise, natural exponential-family models, and certain multiplicative noise models. We also develop a test-time strategy for non-uniform noise with unknown parameters. We further analyze the effect of the recorruption coefficient on denoising error and establish a robustness bound under observation-model mismatch. Extensive experiments demonstrate that R2N outperforms existing self-supervised methods in challenging scenarios involving broader noise models and unknown noise parameters.