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, classically including denoising, deblurring, and sometimes super-resolution, is required before their exploitation. Moreover, quantifying the uncertainty related to this restoration could be valuable by lowering the risk of hallucination and avoiding propagating these biases in downstream applications. Deep learning methods are now state-of-the-art for satellite image restoration. However, they require to train a specific network for each sensor and they do not provide the associated uncertainties. This paper proposes a generic method involving a single network to restore images from several sensors and a scalable way to derive the uncertainties. We focus on deep regularization (DR) methods, which learn a deep prior on target images before plugging it into a model-based optimization scheme. First, we introduce VBLE-xz, which solves the inverse problem in the latent space of a variational compressive autoencoder, estimating the uncertainty jointly in the latent and in the image spaces. It enables scalable posterior sampling with relevant and calibrated uncertainties. Second, we propose the denoiser-based method SatDPIR, adapted from DPIR, which efficiently computes accurate point estimates. We conduct a comprehensive set of experiments on very high resolution simulated and real Pleiades images, asserting both the performance and robustness of the proposed methods. VBLE-xz and SatDPIR achieve state-of-the-art results compared to direct inversion methods. In particular, VBLE-xz is a scalable method to get realistic posterior samples and accurate uncertainties, while SatDPIR represents a compelling alternative to direct inversion methods when uncertainty quantification is not required.