# Deep priors for satellite image restoration with accurate uncertainties

arXiv: https://arxiv.org/abs/2412.04130 · HTML: https://mlsanity.com/paper/2412.04130/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 96 references that are in the map.
- First posted on arXiv 5 Dec 2024.

## Builds on (most cited first, 30 of 56)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Uformer: A General U-Shaped Transformer for Image Restoration](https://mlsanity.com/paper/2106.03106/) (2021)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [CompressAI: a PyTorch library and evaluation platform for end-to-end compression research](https://mlsanity.com/paper/2011.03029/) (2020)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Deep Plug-and-Play Super-Resolution for Arbitrary Blur Kernels](https://mlsanity.com/paper/1903.12529/) (2019)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)

## Built on by (most cited first, 1 of 1)

- [Rethinking Satellite Image Restoration for Onboard AI: A Lightweight Learning-Based Approach](https://mlsanity.com/paper/2604.12807/) (2026)

## Abstract (arXiv)

Satellite optical images, upon their on-ground receipt, offer a distorted view of the observed scene. Their restoration, including denoising, deblurring, and sometimes super-resolution, is required before their exploitation. Moreover, quantifying the uncertainties related to this restoration helps to reduce the risks of misinterpreting the image content. Deep learning methods are now state-of-the-art for satellite image restoration. Among them, direct inversion methods train a specific network for each sensor, and generally provide a point estimation of the restored image without the associated uncertainties. Alternatively, deep regularization (DR) methods learn a deep prior on target images before plugging it, as the regularization term, into a model-based optimization scheme. This allows for restoring images from several sensors with a single network and possibly for estimating associated uncertainties. In this paper, we introduce VBLE-xz, a DR method that solves the inverse problem in the latent space of a variational compressive autoencoder (CAE). We adapt the regularization strength by modulating the bitrate of the trained CAE with a training-free approach. Then, VBLE-xz estimates relevant uncertainties jointly in the latent and in the image spaces by sampling an explicit posterior estimated within variational inference. This enables fast posterior sampling, unlike state-of-the-art DR methods that use Markov chains or diffusion-based approaches. We conduct a comprehensive set of experiments on very high-resolution simulated and real Pl'eiades images, asserting the performance, robustness and scalability of the proposed method. They demonstrate that VBLE-xz represents a compelling alternative to direct inversion methods when uncertainty quantification is required. The code associated to this paper is available in https://github.com/MaudBqrd/VBLExz.