Ising Model for Interpolation of Spatial Data on Regular Grids.

Milan Žukovič,Dionissios T. Hristopulos

doi:10.3390/e23101270

Milan Žukovič, Dionissios T. Hristopulos

Open Access

https://doi.org/10.3390/e23101270

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Abstract

We apply the Ising model with nearest-neighbor correlations (INNC) in the problem of interpolation of spatially correlated data on regular grids. The correlations are captured by short-range interactions between “Ising spins”. The INNC algorithm can be used with label data (classification) as well as discrete and continuous real-valued data (regression). In the regression problem, INNC approximates continuous variables by means of a user-specified number of classes. INNC predicts the class identity at unmeasured points by using the Monte Carlo simulation conditioned on the observed data (partial sample). The algorithm locally respects the sample values and globally aims to minimize the deviation between an energy measure of the partial sample and that of the entire grid. INNC is non-parametric and, thus, is suitable for non-Gaussian data. The method is found to be very competitive with respect to interpolation accuracy and computational efficiency compared to some standard methods. Thus, this method provides a useful tool for filling gaps in gridded data such as satellite images.

Highlights

The current availability of massive remotely sensed georeferenced datasets, pertaining to land cover, terrain elevation, population, meteorological variables, and atmospheric pollution creates increasing demands for efficient processing and analysis methods
The objective of the current study is to investigate the performance of the Ising nearest neighbor correlation (INNC) interpolation method with real datasets of environmental interest, as well as synthetic data
We investigated the Ising model with nearest-neighbor correlations (INNC) interpolation method which can be used to fill gaps in gridded spatial data

Summary

Introduction

The current availability of massive remotely sensed georeferenced datasets, pertaining to land cover, terrain elevation, population, meteorological variables, and atmospheric pollution creates increasing demands for efficient processing and analysis methods. A typical problem is data heterogeneity, i.e., the fact that data are acquired by different modalities, using different methodologies and space-time resolutions. Resolution differences between different sensors as well as data gaps create the missing data problem. In order to apply standard tools for the analysis of space-time earthobservation data, there is a need to fill the gaps and to unify the resolution. These tasks involve downscaling (refining) data with sparse resolution and generating optimal estimates at points without measurements. The mathematical problem of gap filling is interpolation: Estimates of the variable under consideration need to be generated at the target point based on the available data in the vicinity of the target point. Depending on the nature of the modeled variable, interpolation involves either a classification problem (if the values of the variable come from a set of class labels) or regression (if the variable is continuous or if its values are classes that correspond to closed intervals of real numbers)

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