Kriging-based subdivision schemes: Application to the reconstruction of non-regular environmental data

This work is devoted to the construction of new kriging-based interpolating position-dependent subdivision schemes for data reconstruction. Their originality stands in the coupling of the underlying multi-scale framework associated to subdivision schemes with kriging theory. Thanks to an efficient stencil selection, they allow to cope the problem of non-regular data prediction while keeping the interesting properties of kriging operators for the quantification of prediction errors. The proposed subdivision schemes are fully analyzed and an application to the reconstruction of non-regular environmental data is given as well.