Improving in situ data acquisition using training images and a Bayesian mixture model

• A training image-based method is developed for sampling design.
• The method has a sequential nature.
• New samples are extracted from highly uncertain areas.
• A Bayesian mixture model is employed for estimating uncertainty values.
• The method significantly reduced the number of samples required for reconstruction of a field.

Estimating the spatial distribution of physical processes using a minimum number of samples is of vital importance in earth science applications where sampling is costly. In recent years, training image-based methods have received a lot of attention for interpolation and simulation. However, training images have never been employed to optimize spatial sampling process. In this paper, a sequential compressive sampling method is presented which decides the location of new samples based on a training image. First, a Bayesian mixture model is developed based on the training patterns. Then, using this model, unknown values are estimated based on a limited number of random samples. Since the model is probabilistic, it allows estimating local uncertainty conditionally to the available samples. Based on this, new samples are sequentially extracted from the locations with maximum uncertainty. Experiments show that compared to a random sampling strategy, the proposed supervised sampling method significantly reduces the number of samples needed to achieve the same level of accuracy, even when the training image is not optimally chosen. The method has the potential to reduce the number of observations necessary for the characterization of environmental processes.