CNES's Digital Twin Factory project creates coherent virtual representations of Earth's surface, combining space imagery, ground measurements and physical modeling to simulate environmental phenomena including flood modeling, aerosol dispersion, and natural hazard analysis.

These tools require fusing satellite images from multiple modalities. Synthetic Aperture Radar (SAR) images complement optical modalities (multispectral or hyperspectral): optical images are easily interpretable for vegetation characterization, while SAR images excel at detecting structural changes and monitoring natural phenomena (glaciers, volcanoes, earthquakes) with high precision.

However, intrinsic differences between modalities create coherence challenges. RADAR data (amplitude and phase) are decorrelated from spectral reflectance, both modalities exhibit vastly different noise statistics (SAR's multiplicative speckle versus optical noise), and heterogeneous sensors from different missions provide images at variable resolutions with asynchronous acquisitions, amplifying data incoherence.

This thesis addresses geometric registration of heterogeneous satellite imagery. SAR (Sentinel-1, TerraSAR-X, ICEYE) and optical data (Sentinel-2, Pléiades Neo) provide complementary scene views but are often poorly registered. Robust multimodal registration is essential for geo-referencing and joint data exploitation, requiring displacement measurements between source and reference images.

Current pipelines use statistical metrics for registration [4]. For multimodal SAR/optical images, deep neural network approaches have emerged [3] but suffer from end-to-end learning limitations: paired SAR/optical training data remains scarce despite abundant satellite data, and generalization across sensor or scene types is not guaranteed.

We will extend statistical approaches from unimodal data [4]. They are based on two steps: covariance estimation (Sample Covariance Matrix - SCM) and comparison via Kullback-Leibler divergence or mutual information. These tools have explicit solutions only for Gaussian distributions and otherwise rely on computationally expensive estimators. This assumption fails for multimodal data. We will replace the SCM with robust estimators [7] that abstract from distributional assumptions (for symmetric distributions) and integrate structural constraints (low-rank, Kronecker) into estimation algorithms [9].

Next, we will employ metrics based on covariance matrix geometry rather than statistical assumptions, such as log-Euclidean and affine-invariant distances [10]. Those metrics will be more suited to multimodal data but may suffer from several drawbacks: iterative estimation algorithms are computationally expensive with sensitive hyperparameters, and strong dependence on statistical models persists even in non-Gaussian frameworks. To address this, we will leverage unrolled neural networks [6], combining learning and optimization for explainability, efficient training, model robustness, and inference speed. We propose to unroll covariance estimation algorithms [8]. Since these rely on Riemannian gradient descent [5], this represents novel work. In fact, to our knowledge, no unrolling on manifold-based algorithms exists.

A prospective direction involves a single-step approach inspired by metric learning [1], where distances and controlling matrices are learned jointly. This semi-supervised learning suits scenarios with limited annotations. Using [2] as foundation, we will define appropriate registration criteria and unroll the geometric algorithm for enhanced robustness and speed.

We will test our approaches on SAR and optical data from current space missions (Sentinel-1/2, Pléiades Neo, TerraSAR-X, ICEYE), comparing against unimodal methods and neural network approaches [3].

[1] A Bellet et al. A Survey on Metric Learning for Feature Vectors and Structured Data. arXiv:1306.6709, 2014

[2] M Harandi et al. Joint Dimensionality Reduction and Metric Learning: A Geometric Take. ICML 2017

[3] LH Hughes et al. A deep learning framework for matching of SAR and optical imagery. ISPRS JPRS 169, 2020

[4] J Inglada et al. On the possibility of automatic multisensor image registration. IEEE TGRS 42(10), 2004

[5] A Mian et al. Online change detection in SAR time-series with Kronecker product structured scaled Gaussian models. Signal Process 224, 2024

[6] V Monga et al. Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing. IEEE SPM 38(2), 2021

[7] E Ollila et al. Complex Elliptically Symmetric Distributions: Survey, New Results and Applications. IEEE TSP 60(11), 2012

[8] C Pouliquen et al. Schur's Positive-Definite Network: Deep Learning in the SPD cone with structure. ICLR 2025

[9] Y Sun et al. Low-Complexity Algorithms for Low Rank Clutter Parameters Estimation in Radar Systems. IEEE TSP 64(8), 2016

[10] Y Thanwerdas et al. O(n)-invariant Riemannian metrics on SPD matrices. Linear Algebra Appl 661, 2022

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For more Information about the topics and the co-financial partner (found by the lab !); contact Directeur de thèse -guillaume.ginolhac@univ-smb.fr

Then, prepare a resume, a recent transcript and a reference letter from your M2 supervisor/ engineering school director and you will be ready to apply online  before March 13th, 2026 Midnight Paris time !