ZHOU, Jialun; SAID, Salem; BERTHOUMIEU, Yannick

doi:10.1016/j.sigpro.2021.108376

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ZHOU, Jialun

Laboratoire de l'intégration, du matériau au système [IMS]

SAID, Salem

Laboratoire de l'intégration, du matériau au système [IMS]

BERTHOUMIEU, Yannick
Laboratoire de l'intégration, du matériau au système [IMS]

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Signal Processing. 2022-03, vol. 192, p. 108376

Résumé en anglais

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 applications, to image re-colorization, and to texture classification, are also worked out.< Réduire

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Elliptically-contoured distribution

Riemannian information gradient

Large-scale dataset

Image re-colorization

Texture classification

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Riemannian information gradient methods for the parameter estimation of ECD

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