Reconstruction of Gaussian regular sampled fields with jitter

In this paper, we analyse the optimal regular Sampling - Reconstruction Procedure of Gaussian fields with jitter and a limited number of samples. The proposed methodology is based on the conditional mean rule and on the statistical average operation with respect to the random position of samples. With this method, we find some advantage, for instances, we obtain the surfaces of the optimal error reconstruction functions in the whole space domain. Furthermore, we investigate different cases, i.e., when: 1) the jitter is only presented in some samples; 2) the jitter of each sample is independent; 3) the jitter can be described by the same or different features. The jitter is characterized by the McFadden's distribution and depending of its parameters, we consider the circular and the elliptical distribution. We demonstrate how diverse factors influence on the principal optimal SRP characteristics such as: the covariance functions; the position of the samples; the number of samples; the distances between samples; and the symmetry between the axes of the covariance function.