ED Sciences Physiques et de l'Ingénieur
Change detection and classification in time series of multi-dimensional satellite images
by Rémi BEISSON (Laboratoire de l'Intégration du Matériau au Système)
The defense will take place at 10h00 - Amphithéâtre JP DOM UMR 5218 - IMS - Laboratoire de l'Intégration du Matériau au Système 351 Cours de la Libération, 33405 Talence Cedex, France
in front of the jury composed of
- Audrey GIREMUS - Professeure des universités - Université de Bordeaux - Directeur de these
- Nicolas LE BIHAN - Directeur de recherche - GIPSA, Université Grenoble Alpes - Rapporteur
- François VINCENT - Professeur des universités - ISAE-SupAero, Université de Toulouse - Rapporteur
- Frédéric PASCAL - Professeur des universités - CentraleSupelec, Université Paris Saclay - Examinateur
- Florent BOUCHARD - Chargé de recherche - L2S, Université Paris Saclay - Examinateur
This thesis focuses on change detection in multidimensional time series of satellite images. Specifically, we address the equality test of covariance matrices in the context of multivariate complex Gaussian time series. The covariance matrices of $L$ time series, each of dimension $M$, are modeled as rank-$K$ perturbations of the identity matrix, representing a signal-plus-noise model. In this research, we propose a novel test statistic based on estimates of the eigenvalues of covariance matrices. This test statistic is consistent in the asymptotic regime of large dimensions, where the sample sizes $N_1, dots, N_L$ for each time series and the dimension $M$ approach infinity at the same rate, while keeping $K$ and $L$ fixed. Additionally, we provide a control of the Type I error of the proposed test statistic in the asymptotic regime of large dimensions. Simulations on simulated data and real-world data have demonstrated rather satisfactory results compared to other relevant methods, even for moderate values of $M$ and $N_1, dots, N_L$.