Deep priors for satellite image restoration with accurate uncertainties

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 Pléiades 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.

💡 Research Summary

Satellite optical images suffer from noise, blur, and compression artifacts that degrade their usefulness for downstream remote‑sensing tasks. While deep learning‑based direct inversion methods have become the de‑facto standard for image restoration, they require a dedicated network for each sensor and typically provide only point estimates, lacking any measure of confidence. This paper proposes VBLE‑xz, a deep‑regularization (DR) framework that restores images and simultaneously quantifies uncertainties. VBLE‑xz operates in the latent space of a variational compressive auto‑encoder (CAE). A single high‑bitrate CAE is trained once; during inference the effective bitrate is adjusted without further training, allowing the regularization strength to adapt automatically to varying degradation levels (noise, blur, compression).

The key methodological advance over the earlier VBLE is the joint modeling of the posterior distribution over both latent variables z and the image x. Using variational inference, the authors derive an evidence lower bound (ELBO) that incorporates the data‑likelihood term −log p(y|x) and a hyper‑prior on z. Sampling from the approximate posterior is achieved by drawing z from qϕ(z|y) and passing it through the decoder pθ(x|z), yielding fast posterior samples without the costly iterations required by MCMC or diffusion‑based samplers.

Experiments are conducted on realistic simulated degradations and on real Pléiades‑HR panchromatic images. The evaluation includes standard restoration metrics (PSNR, SSIM, LPIPS) and uncertainty metrics (negative log‑likelihood, calibration error, expected calibration error). VBLE‑xz matches or exceeds state‑of‑the‑art DR methods such as PG‑DPIR and MCMC‑ULA in restoration quality, while delivering significantly more accurate uncertainty estimates. Computationally, VBLE‑xz is 5–10× faster than MCMC approaches and comparable to deterministic DR pipelines. Compared with direct inversion networks, VBLE‑xz offers slightly lower PSNR but avoids hallucinated structures and, crucially, provides calibrated confidence intervals that correlate strongly with true reconstruction errors—an essential feature for risk‑aware applications like object detection or change monitoring.

The authors release the code and pretrained models, demonstrating reproducibility and paving the way for broader adoption of DR techniques in high‑resolution satellite image processing. VBLE‑xz thus represents a compelling alternative to sensor‑specific direct inversion, delivering both high‑quality restoration and reliable uncertainty quantification with modest computational overhead.