Estimation of anisotropic Gaussian fields through Radon transform

Issue		ESAIM: PS Volume 12


Page(s)		30 - 50
DOI		10.1051/ps:2007031
Published online		13 November 2007

ESAIM: P&S, 2008, Vol. 12, p. 30-50
DOI: 10.1051/ps:2007031

Estimation of anisotropic Gaussian fields through Radon transform

Hermine Biermé and Frédéric Richard

MAP5-UMR 8145, Université René Descartes45, rue des Saints-Pères, 75270 Paris cedex 06 France, hermine.bierme@math-info.univ-paris5.fr; frederic.richard@math-info.univ-paris5.fr

Received February 15, 2006. Revised December 12, 2006. Published online 13 November 2007

Abstract
We estimate the anisotropic index of an anisotropic fractional Brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional Brownian field and prove that these processes admit a spectral density satisfying the previous assumptions. Finally we use simulated fields to test the proposed estimator in different anisotropic and isotropic cases. Results show that the estimator behaves similarly in all cases and is able to detect anisotropy quite accurately.

Mathematics Subject Classification. 60G60, 62M40, 60G15, 60G10, 60G17, 60G35, 44A12

Key words: Anisotropic Gaussian fields, identification, estimator, asymptotic normality, Radon transform.

© EDP Sciences, SMAI 2008

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