Self-Supervised Uncertainty Estimation For Super-Resolution of Satellite Images

Zhe Zheng; Valéry Dewil; Pablo Arias

cs.CVMar 14, 2026

Self-Supervised Uncertainty Estimation For Super-Resolution of Satellite Images

Authors: Zhe Zheng, Valéry Dewil, Pablo Arias

Organizations: Centre Borelli, ENS Paris-Saclay, Universite Paris-Saclay, CNRS, Gif-sur-Yvette, France · Dept. of Engineering, Universitat Pompeu Fabra, Barcelona, SPAIN

Abstract

Super-resolution (SR) of satellite imagery is challenging due to the lack of paired low-/high-resolution data. Recent self-supervised SR methods overcome this limitation by exploiting the temporal redundancy in burst observations, but they lack a mechanism to quantify uncertainty in the reconstruction. In this work, we introduce a novel self-supervised loss that allows to estimate uncertainty in image super-resolution without ever accessing the ground-truth high-resolution data. We adopt a decision-theoretic perspective and show that minimizing the corresponding Bayesian risk yields the posterior mean and variance as optimal estimators. We validate our approach on a synthetic SkySat L1B dataset and demonstrate that it produces calibrated uncertainty estimates comparable to supervised methods. Our work bridges self-supervised restoration with uncertainty quantification, making a practical framework for uncertainty-aware image reconstruction.

Figures & tables

Figure 1: We propose a self-supervised strategy to train a network that performs super-resolution with uncertainty quantification in satellite imaging. The network is purely trained using noisy and low-resolution data, without requiring high-resolution ground truth. Left : four input images out of a burst of multi-exposure, low-resolution and noisy images; Center : Reconstruction results (top) and estimated uncertainty (bottom) by the self-supervised network and by the supervised one; high resolution ground truth (top) and reconstruction error by the self-supervised method. Right : comparison of the coverage test for the estimated uncertainty (variance of posterior distribution) with the self-supervised and supervised training.

Figure 2: Data flow during training. The optical flows

\{F_{t}\}_{i=2}^{N}

are substracted first by the shift

\mathcal{S}_{\tau}

and then sent to the network together with the burst LR observations

\{v_{t}\}_{i=2}^{N}

. The super-resolved image

\hat{u}(v)

and

\hat{\Sigma}

are shifted by

\mathcal{S}_{\tau}

and then downsampled to compute loss with the reference

v_{1}

Methods	self-sup.	supervised
$\hat{\mu}(v)$ PSNR	54.05	54.24
$\hat{\nu}(v)$ V-RMSE ( $\times 10^{-5}$ )	2.50	2.51
$\hat{\nu}(v)$ sharpness ( $\times 10^{-3}$ )	5.29	5.81

Table 1: Evaluation of the estimates for both reconstruction and uncertainty estimate.

Metrics	self-sup.		supervised
V-RMSE ( $\times 10^{-5}$ )	0.79	1.90	0.86	1.87
V-RMSE ( $\times 10^{-5}$ )	1.80	1.75	2.04	1.71
ECE	0.060	0.041	0.021	0.023
ECE	0.038	0.032	0.024	0.027
Sharpness ( $\times 10^{-3}$ )	4.22	5.49	5.04	6.00
Sharpness ( $\times 10^{-3}$ )	5.81	5.63	6.31	5.89

Table 2: Comparison of uncertainty estimates for pixels from different positions. For each metric we show four values corresponding to the pixels in the four sets: top left, top right, bottom left, bottom right. The estimates for the top-left pixel has the smallest RMSE and the smallest estimated

\hat{\nu}

in all four methods. Pixels from this position are used to generate LR samples.

Image Super-Resolution

Image super-resolution reconstructs high-resolution images from lower-resolution observations, balancing detail, fidelity, and computational cost.

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Self-Supervised Super-Resolution for Sentinel-5P Hyperspectral Images

Hyam Omar Ali, Antoine Crosnier, Romain Abraham, Baptiste Combelles+2

Université d’Orléans, Université de Tours, CNRS, IDP, UMR 7013, Orléans, France · Faculty of Mathematical Sciences, University of Khartoum, Sudan · ENS Lyon, France+2

Self-Supervised Learning Remote Sensing Image Super-Resolution Hyperspectral Image Super-Resolution Remote Sensing Hyperspectral Imaging Image Super-Resolution

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Sentinel-5P (S5P) plays a critical role in atmospheric monitoring; however, its spatial resolution limits fine-scale analysis. Existing super-resolution (SR) approaches rely on supervised learning with synthetic low-resolution (LR) data, since true high-resolution (HR) data do not exist, limiting their applicability to real observations. We propose a self-supervised hyperspectral SR framework for S5P that enables training without HR ground truth. The method combines Stein's Unbiased Risk Estimator (SURE) with an equivariant imaging constraint, incorporating the S5P degradation operator and noise statistics derived from signal-to-noise ratio (SNR) metadata. We also introduce depthwise separable convolution U-Net architectures designed for efficiency and spectral fidelity. The framework is evaluated in two settings: (i) LR-HR, where synthetic LR data are used for direct comparison with supervised learning, and (ii) GT-SHR, where super-resolved images surpass the native spatial resolution without HR reference. Results across multiple bands show that self-supervised models achieve performance comparable to supervised methods while maintaining strong consistency. Qualitative analysis shows improved spatial detail over bicubic interpolation, and validation with EMIT data confirms that reconstructed structures are physically meaningful. Code is available at https://github.com/hyamomar/Sentinel-5P-Super-Resolution/tree/main/self_supervised

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Image Super-Resolution

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