Construction and Analysis of Zone-dependent Interpolatory/Non-interpolatory Stochastic Subdivision Schemes for Non-regular Data

Abstract

This work is devoted to the definition of stochastic subdivision schemes adapted to the reconstruction of non-regular data. These schemes are constructed in the framework of the Kriging theory. Thanks to the introduction of a zone-dependent error variance in the Kriging approach, they combine interpolatory and non interpolatory subdivision schemes according to a domain segmentation. Their originality relies on the introduction and coupling of three ingredients: a segmentation of the data, a local prediction according to the characteristics of the different zones and an adaption strategy near segmentation points. The convergence of the corresponding 4-point scheme is analyzed. Its behavior is compared with other subdivision schemes on various numerical experiments.