Wavelet-based Resampling Techniques

Wavelet-based Resampling Techniques investigated the application of the wavelet transform to dependent data. Such data naturally arise in time series and point processes either in one or two dimensions. While standard wavelet transforms can be applied to time series or one-dimensional point processes they need to be adapted to two-dimensional processes. This thesis developed a method based on Delaunay triangulation to remove points one at a time in a similar way to the wavelet lifting algorithm. The technique was applied to Poisson point processes clustered data non-homogeneous point processes and marked data.