An l1-regularized total variation minimization model for soil interpolation based on geostatistical priors

Abstract

Geostatistical interpolation of soil properties is highly demanded to assess the status of soil conditions. Recently, methods based on compressed sensing (CS) have been developed to improve the interpolation results to handle cases of limited observations. Here, we used the total variation, an equivalent concept of spatial autocorrelation, to modify the conventional CS interpolation model (CS-V) for soil science and form a new model, l1-TV. The spatial structure information in the variogram models was taken as geostatistical priors to produce ideal results. Examples of interpolation of soil electrical conductivity and heavy metals content were employed to validate and illustrate this new model. A comparison of the interpolation results of ordinary kriging (OK), CS-V and l1-TV showed that the CS method had an advantage over OK when the spatial correlation of soil properties was strong. A significant improvement in l1-TV was also exhibited; that is, the new model can provide more stable performance and show good adaptability to changes in soil spatial correlation. Furthermore, the generation of soil maps from a large number of environmental variables within the l1-TV framework is a promising application for further research.