Adaptation of regular grid filterings to irregular grids

This note is about filtering and subsampling of signals sampled on irregular sampling points. The number of filters and wavelets available in the litterature on regular grids is far higher than on irregular grids, because the filtering scheme is uniform and can be efficiently examined by means of a Fourier transform or a z-transform. What is described here is how to adapt a filtering scheme designed for regular grids to irregular grids. The filtering and subsampling process is decomposed into lifting steps, and then each of the steps are adapted to the irregular grid structure.