Gaussian processes-based sampling for scalar field reconstruction considering gradient information

Abstract

We are surrounded by several natural phenomena, which can be studied by reconstructing the field underlying these phenomena for research purposes as a good approach. The field can be restructured accurately because of developments in sensor measurement technology and regression techniques. If the number of sensors required to identify the field is larger than the number of available sensors, it is necessary to identify the optimal locations to which to allocate sensors for reconstruction of the field. Criteria based on uncertainty have been used widely. However, the even distribution of sampling points across the entire field has the disadvantage of reducing the amount of sampling in areas that are particularly informative. We overcome this limitation by suggesting a new criterion that combines gradient information, uncertainty, and an algorithm to control the trade-off between exploitation and exploration. The results are given in terms of sampling locations and the root mean square error between the underlying field and the estimated field. The proposed algorithm increases the amount of sampling that occurs in an informative area, and also ensures that the error is lower compared to the other criteria. Consequently, the proposed algorithm has confirmed the possibility of identifying the informative area.