Integrating Data Uncertainty in Multiresolution Analysis

Multiresolution decomposition frameworks are instrumental when one needs to focus data analysis at a particular scale or to separate the several contributions to the overall phenomenon, arising from different scales either in time or length. On the other hand, measurement uncertainties are now frequently available along with raw value measurements. In this paper we address the development of multiresolution decomposition methodologies that are able to cope with difficult data/uncertainty structures often met in industrial practice, like missing data and heteroscedastic uncertainties. A guideline is provided regarding their adequate use and an example illustrates the potential benefits associated with the suggested approach.