Scalar Field Reconstruction Based on the Gaussian Process and Adaptive Sampling

Abstract

This paper proposes a method of reconstructing a scalar field by adaptively choosing sampling locations and using the measurements obtained from those locations to reconstruct an estimate of the underlying field using Gaussian process regression. Spreading sampling points evenly over the field may not always be effective if the field is not uniformly distributed and the maximum number of measurements is limited. Taking more measurements in regions of large changes in the field than in regions of small changes can give a better estimate than spreading the same number of measurements evenly over the space. The proposed algorithm was tested on a synthetic scalar field and corn pared to two popular methods of determining sensor placement based on entropy and mutual information from information theory.