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

Zhe Zheng, Valéry Dewil, Pablo Arias

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.

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

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.
Paper Structure (19 sections, 3 theorems, 29 equations, 2 figures, 2 tables)

This paper contains 19 sections, 3 theorems, 29 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Self-Supervised MISR
  5. Degradation model for satellite MISR.
  6. Network architecture.
  7. Self-supervised loss.
  8. Self-Supervised Gaussian NLL Loss
  9. Estimation of ${\hat{R}_\tau(v)}$.
  10. Optimal estimators
  11. Subsampling matrix $A_\tau$.
  12. Experiments
  13. Quantitative evaluation
  14. Coverage under a Gaussian probabilistic model.
  15. Qualitative evaluation
  16. ...and 4 more sections

Key Result

Lemma 4.1

Assume that $\tau$ and $u$ are conditionally independent given v and $z = A_\tau u + n$, where $n$ is zero mean additive noise with signal dependent variance. Denote Then estimators $\hat{u}(v)$ and ${\hat{\Sigma}(v)}$ that minimize the self-supervised risk eq:risk_full_conditional verify the following conditions:

Figures (2)

  • 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 $v_1$.

Theorems & Definitions (7)

  • Lemma 4.1: Full covariance and general linear degradation.
  • proof
  • Lemma 4.2: Diagonal covariance a nd general linear degradation
  • proof
  • Proposition 4.3: Diagonal covariance and subsampling degradation
  • proof
  • Remark