Context

Remote sensing data from Synthetic Aperture Radar (SAR) sensors offer a unique opportunity to record, analyze, and predict the evolution of the Earth’s surface. In the last decade, numerous satellite remote sensing missions have been launched (Sentinel-1, UAVSAR, TerraSAR X, etc.) resulting in a tremendous improvement in image acquisition capability and accessibility. The growing number of observation systems allows now to build images datasets with high spatio-temporal resolution and raises the interest in time series processing to monitor changes occurring over large areas, in particular for applications such as forest, glacier or urbanization monitoring, and land activity surveillance.

On the other hand, this massive data volume is currently a challenge for developing new algorithms; in particular, modern supervised learning based approaches, such as deep learning, may not be relevant since most of the available data remain unlabelled and corrupted by a speckle noise. To perform change detection and classification in time series of images, statistical learning methods which leverage probabilistic models integrating physical prior knowledge, appear more relevant in this context. Moreover, due to the high spatio-temporal resolution of the available images, new methods which fully exploit the high dimensionality of the data and significantly improve the performance in terms of resolution, probability of correct detection or identification, are needed. However, the direct use of classical statistical learning methods do not lead to the expected performance gain, for two main reasons:

(1) they often rely on the sample covariance matrix of the data, which is a poor estimate in the context of high dimensional data;
(2) the environment response (clutter) is more complex and heterogeneous, involving a significant discrepancy with the Gaussian model traditionally used.

Different solutions have been proposed during the past few years to overcome these issues, such as the use of robust covariance estimates [6, 2], covariance shrinkage estimates [8, 11, 7], the use of covariance estimates based on a a priori knowledge of data structure [16, 14], or the use of spectral projections instead of covariance matrices.

Nevertheless, although these recent methods form a starting point to solve the heterogeneous environment and large dimension issues, they may induce some important drawbacks: the CFAR (Constant False Alarm Rate) property for detectors is usually not verified anymore; some methods are function of parameters (shrinkage coefficient, subspace rank, etc.) whose estimation may be tricky; the performance is hard to study with standard statistical tools.

Objectives

The first goal of this thesis is to develop new statistical methods for change detection in high-dimensional time series of images, having key properties such as CFAR or robustness to the data distribution and hyperparameters. The starting point will be based on the works of [4, 3, 10], and improvements in a high-dimensional context will be proposed using tools from high-dimensional statistics [15, 1, 13].

The second goal of the thesis is focused on change signature identification (appearance, disappearance, slow evolution) within the statistical learning framework. New clustering methods will be proposed relying on metrics between covariance matrices or spectral projections [5, 9, 12], and designed for high-dimensional and heterogeneous data.

Finally, the proposed methods and theoretical results will be assessed on high definition SAR images (such as SANDIA, UAVSAR, PASTIS) as well as hyperspectral images.

Candidate profile

The candidate must have the equivalent of a Master’s degree in the field of signal and image processing, applied mathematics or data science. A solid background in statistics or machine learning is required, as well as programming skills in Python. Fluency in English and good writing skills are also required.

Information and contact

The Ph.D will start in October 2024 and will take place in the Laboratoire de l’Intégration du
Matériau au Système (IMS) at Bordeaux University, with the following supervisory team:
• Pr. Pascal Vallet, IMS/Bordeaux INP,
• Pr. Audrey Giremus IMS/Bordeaux INP
• Pr. Guillaume Ginolhac, LISTIC/Polytech Annecy.

Applicants must send via e-mail to { pascal.vallet@ims-bordeaux.fr, audrey.giremus@ims-bordeaux.fr, guillaume.ginolhac@univ-smb.fr } a CV as well as a transcript of the last year study. Recommendation letters will be a plus.

References

[1] R. Beisson, P. Vallet, A. Giremus, and G. Ginolhac. Change detection in the covariance structure of high-dimensional Gaussian low-rank models. In 2021 IEEE Statistical Signal Processing Workshop (SSP), pages 421–425. IEEE, 2021.
[2] A. Breloy, G. Ginolhac, F. Pascal, and P. Forster. Robust covariance matrix estimation in low rank heterogeneous noise context. IEEE Trans. Signal Process., 64(22):5794 – 5806, 2016.
[3] D. Ciuonzo, V. Carotenuto, and A. De Maio. On multiple covariance equality testing with application to SAR change detection. IEEE Trans. Signal Process., 65(19):5078 – 5091, October 2017.
[4] K. Conradsen, A.A. Nielsen, and H. Skriver. Determining the points of change in time series of polarimetric SAR data. IEEE Trans. on Geo. and Rem. Sens., 54(5):3007 – 30024, May 2016.
[5] Masoud Faraki, Mehrtash T Harandi, and Fatih Porikli. More about vlad: A leap from euclidean to riemannian manifolds. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 4951–4960, 2015.
[6] G. Ginolhac, P. Forster, F. Pascal, and J.P. Ovarlez. Exploiting persymmetry for low-rank space time adaptive processing. Signal Processing, 97(4):242 – 251, April 2014.
[7] A. Kammoun, R. Couillet, F. Pascal, and M-S Alouini. Optimal adaptive normalized matched filter for large antenna arrays. IEEE Trans. on Aero. and Elec. Syst., Accepted 2017.
[8] O. Ledoit and M. Wolf. A well-conditioned estimator for large-dimensional covariance matrices. Journal of multivariate analysis, 88:365–411, 2004.
[9] John Lipor, David Hong, Dejiao Zhang, and Laura Balzano. Subspace clustering using ensembles of k-subspaces. arXiv preprint arXiv:1709.04744, 2017.
[10] A. Mian, J.P. Ovarlez, G. Ginolhac, and A. Atto. A new change detector for highly heterogeneous multivariate images. In ICASSP, Calgary, Canada, April 2018.
[11] F. Pascal, Y. Chitour, and Yihui Quek. Generalized robust shrinkage estimator and its application to stap detection problem. Signal Processing, IEEE Transactions on, 62(21):5640–5651, 2014.
[12] S. Said, L. Bombrun, Y. Berthoumieu, and J. Manton. Riemannian gaussian distributions on the space of symmetric positive definite matrices. IEEE Trans. Inf. Theory, 63(4):2153–2170, 2017.
[13] A. Steland. Testing and estimating change-points in the covariance matrix of a high-dimensional time series. J. Multivar. Anal., 177:104582, 2020.
[14] Y. Sun, A. Breloy, P. Babu, D.P. Palomar, F. Pascal, and G. Ginolhac. Robust estimation of structured covariance matrix for heavy-tailed elliptical distributions. IEEE Trans. Signal Process., 64(14):3576–3590, 2016.
[15] P. Vallet, X. Mestre, and P. Loubaton. Performance Analysis of an Improved MUSIC DoA Estimator. IEEE Trans. Signal Process., 63(23):6407–6422, December 2015.
[16] A. Wiesel. Unified framework to regularized covariance estimation in scaled Gaussian models. IEEE Trans. Signal Process., 60(1):29–38, 2012.