On the least squares estimator asymptotic normality of the multivariate symmetric textured surface parameters

Abstract

A multivariate trigonometric regression model is considered. Various discrete modifications of the similar bivariate model received serious attention in the literature on signal and image processing due to multiple applications in the analysis of symmetric textured surfaces. In the paper asymptotic normality of the least squares estimator for amplitudes and angular frequencies is obtained in multivariate trigonometric model assuming that the random noise is a homogeneous or homogeneous and isotropic Gaussian, in particular, strongly dependent random field on  R M , M > 2. \mathbb {R}^M,\,\, M>2.