Estimating deformations of isotropic Gaussian random fields on the plane

TL;DR

This paper introduces a new method for estimating deformations in isotropic Gaussian random fields on the plane, enabling the recovery of nonstationary processes from single observations.

Contribution

It provides a comprehensive framework and algorithms for identifying and estimating deformations of isotropic Gaussian fields based on dense single-realization data.

Findings

Effective deformation estimation from dense observations

Complete methodological package from assumptions to algorithms

Applicable to nonstationary Gaussian processes

Abstract

This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on $\mathbb{R}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we investigate the identification and estimation of deformations. We then present a complete methodological package--from model assumptions to algorithmic recovery of the deformation--for the class of nonstationary processes obtained by deforming isotropic Gaussian random fields.