Interpolation of soil properties from geostatistical priors and DCT-based compressed sensing

The distribution of and variation in soil properties are spatially correlated and commonly obtained through interpolation techniques and point source surveys. The contradiction between sample limitation and data demand has become an obstacle to generating accurate distribution maps with conventional methods, such as geostatistical or machine learning methods. To weaken the negative impact of limited data and obtain a more accurate distribution map, we introduce a new interpolation method called CS-V into soil science. The method combines compressed sensing (CS), which is a novel signal recovery technique, with the traditional geostatistical prior and generates a distribution map by solving a sparse recovery problem. Two datasets, a complete measurement set of soil electrical conductivity (EC) and a discrete point set of soil organic matter (SOM), were used to validate the feasibility and investigate the characteristics of the method. The compressibility of the soil distribution map was first validated through the EC dataset to provide the fundamentals of CS-V. The comparison between the results of CS-V and ordinary kriging (OK) shows that CS-V can provide a higher prediction accuracy and a wider estimation range. In addition, considering the two parameters of the sparse recovery problem, the regularized parameter lambda is the decisive factor that controls the interpolation results, and the influence of searching space k is diluted when lambda is large enough. The CS-V method is suitable as an alternative interpolation method in soil science in the case of limited measurement data.