https://hal.science/hal-03866181Zhou, JialunJialunZhouSaid, SalemSalemSaidIMS - Laboratoire de l'intégration, du matériau au système - UB - Université Sciences et Technologies - Bordeaux 1 - Institut Polytechnique de Bordeaux - CNRS - Centre National de la Recherche ScientifiqueBerthoumieua, YannickYannickBerthoumieuaRiemannian information gradient methods for the parameter estimation of ECD : Some applications in image processingHAL CCSD2022elliptically-contoured distributionRiemannian information gradientlarge-scale datasetimage re-colorizationtexture classification[STAT.OT] Statistics [stat]/Other Statistics [stat.ML][MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]Said, Salem2022-11-22 16:07:372023-03-24 14:53:292022-11-30 15:16:52enJournal articleshttps://hal.science/hal-03866181/document10.1016/j.sigpro.2021.108376application/pdf1Elliptically-contoured distributions (ECD) play a significant role, in computer vision, image processing, radar, and biomedical signal processing. Maximum likelihood estimation (MLE) of ECD leads to a system of non-linear equations, most-often addressed using fixed-point (FP) methods. Unfortunately, the computation time required for these methods is unacceptably long, for large-scale or high-dimensional datasets. To overcome this difficulty, the present work introduces a Riemannian optimisation method, the information stochastic gradient (ISG). The ISG is an online (recursive) method, which achieves the same performance as MLE, for large-scale datasets, while requiring modest memory and time resources. To develop the ISG method, the Riemannian information gradient is derived taking into account the product manifold associated to the underlying parameter space of the ECD. From this information gradient definition, we define also, the information deterministic gradient (IDG), an offline (batch) method, which is an alternative, for moderate-sized datasets. The present work formulates these two methods, and demonstrates their performance through numerical simulations. Two