hal-03866181
https://hal.science/hal-03866181
https://hal.science/hal-03866181/document
https://hal.science/hal-03866181/file/SIGPRO.pdf
doi:10.1016/j.sigpro.2021.108376
[CNRS] CNRS - Centre national de la recherche scientifique
[IMS-BORDEAUX] Laboratoire de l'intégration, du matériau au système
[INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions
[IMS-BORDEAUX-FUSION] Laboratoire de l'intégration, du matériau au système TOUS LABOS
Riemannian information gradient methods for the parameter estimation of ECD : Some applications in image processing
Zhou, Jialun
Said, Salem
Berthoumieua, Yannick
[STAT.OT] Statistics [stat]/Other Statistics [stat.ML]
[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
ART
elliptically-contoured distribution
Riemannian information gradient
large-scale dataset
image re-colorization
texture classification
Elliptically-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
2022
2022-11-22
en
Signal Processing
Elsevier