THESIS DEFENSE OF Rémi BEISSON - MAY 28, 2024

Rémi BEISSON will defend his thesis on May 28th, 2024 at 10:00 am in the Amphi JP. DOM from the IMS laboratory on the subject : “Change detection in multi-dimensional satellite image time series”.

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 $N_1, \dots, N_L$.