Probabilistic Reconstruction of Sentinel-2 Satellite Image Time Series Using Multi-Sensor Gaussian Process Models

Satellite Image Time Series (SITS) are a cornerstone of Earth observation, enabling long-term monitoring of environmental processes such as vegetation dynamics, land-use change, and natural hazards. However, optical satellite time series, including Sentinel-2, are frequently irregular and incomplete due to cloud cover, atmospheric effects, and acquisition constraints, which strongly limit their usability in operational monitoring systems. In contrast, Sentinel-1 Synthetic Aperture Radar (SAR) provides regular observations for any weather condition and offers complementary information for mitigating optical sensor limitations. Generating dense and reliable Sentinel-2 time series from multi-sensor observations therefore remains a critical challenge.

This work investigates Gaussian Process (GP) based statistical models for the reconstruction and densification of Sentinel-2 image time series by jointly exploiting Sentinel-1 and Sentinel-2 data. Gaussian Processes offer a flexible Bayesian framework for pixel interpolation and extrapolation. We explore GP formulations capable of handling irregular temporal sampling, multi-output dependencies, and latent variable structures, enabling the fusion of heterogeneous optical and radar observations.

An in-depth analysis of the state-of-the-art is conducted, covering multi-output Gaussian Processes, sparse and variational approximations for scalability, latent variable models (including hierarchical GP-LVMs), and inverse GP approaches based on shared latent spaces. These methods are evaluated with respect to three key challenges: ensuring spatio-temporal coherence of reconstructed images, fusing asynchronous multi-sensor observations, and maintaining computational tractability for large-scale satellite datasets.

To support experimental investigations, a representative multi-regional dataset is constructed over mainland France and overseas territories, capturing diverse climatic patterns, land-cover types, and cloud conditions, including extreme events such as flooding. 

This study establishes the methodological foundations for reconstructing dense Sentinel-2 time series conditioned on Sentinel-1 observations, with explicit uncertainty quantification. By leveraging Sentinel-1 data, the approach effectively imputes missing Sentinel-2 values while providing consistent average pixel estimates with associated uncertainty, which is critical for geoscience applications. The proposed framework contributes toward more robust Earth observation monitoring systems and the development of reliable geospatial digital twins.