Convexity-Aware Noise Calibration: A Self-Supervised Framework for Noise-Level-Unknown Image Denoising

Image denoising is a fundamental task in computer vision aimed at recovering clean images from noise-corrupted observations. While supervised deep learning methods achieve remarkable performance when trained on paired data with known noise levels, their real-world applicability is limited as noise characteristics are often unknown. Existing unsupervised techniques, such as blind-spot networks or methods based on statistical estimation, either compromise performance due to information loss or suffer from inaccuracies in noise level estimation. To address these challenges, we propose a novel two-stage self-supervised denoising framework that first accurately estimates the noise level directly from noisy images, without requiring clean references or prior noise knowledge. Building upon theoretical insights from Noisier2Noise, we rigorously derive a relationship between the noise level and the variance of the denoised image, enabling robust estimation via a deep learning model and a ternary search strategy. The estimated noise level is then used to synthesize training pairs for supervised denoising. Experiments demonstrate that our method outperforms existing unsupervised approaches and traditional noise estimation techniques, achieving performance competitive with—and in some cases surpassing—supervised methods trained with known noise levels. The proposed framework effectively overcomes the training data pair limitations of supervised approaches for unknown additive white Gaussian noise. Our code will be available.