Uncertainty Estimation Optimization for Reliable Remote Sensing Single-Image Super-Resolution

Remote sensing(RS) single-image super-resolution (SISR) is a classic ill-posed problem in low-level vision, characterized by a one-to-many mapping. This ill-posedness can lead to aleatoric uncertainty, thereby rendering the reconstruction results unreliable. Given that remote sensing images typically carry strict physical significance, quantifying uncertainty to evaluate pixel-wise reliability in RSSISR results is of critical importance. In this paper, we estimate image uncertainty based on differential entropy under a given assumed data distribution, and propose a general framework that integrates uncertainty into the loss function for SISR. Within this framework, we derive various uncertainty-aware loss functions under commonly assumed distributions. However, the learning of uncertainty in these loss functions is performed in an unsupervised manner, which frequently results in instability during training. To address this, we design an uncertainty estimation branch incorporating a sparse prior and introduce a similarity measure based on perceptual space features, thereby enhancing the stability of the uncertainty learning process. To mitigate the issue of loss attenuation caused by assigning lower weights to high-uncertainty pixels during uncertainty learning, we introduce an uncertainty-guided loss function after the uncertainty estimation stage. This loss function assigns greater importance to high-uncertainty pixels, thereby enhancing the reconstruction quality and reliability of the SISR results. Our proposed framework can be seamlessly integrated into popular SISR networks, enabling the simultaneous generation of high-quality SR images and reliable uncertainty maps. Extensive experiments demonstrate that our method outperforms existing state-of-the-art approaches in terms of reconstruction accuracy and perceptual quality, while simultaneously preserving meaningful uncertainty estimates. The corresponding code is available at: https://github.com/yaoxudong241/UEO.