Characterization of local and global regularity by the continuous wavelet transform, applied to real and synthetic data

This FFI Report is a reprint, with some minor bug-fixes, of my Cand. Scient. Thesis with the same title at The University of Oslo, Mathematics Department, spring 2006. Some important Theorems regarding the connection between the decay of the Wavelet Transform across scales and the regularity of functions, locally and globally, will be presented and proved, and an algorithm for computing the local regularity of functions based on the WTMM (Wavelet Transform Modulus Maxima) methods derived from these Theorems will be described and used on a Laser Altimetry data set.