Exploiting Wavelet Coefficients for Modifying Functions

Abstract

Various methods have been developed to modify and model functions. Even so, we found it worth while to consider a further one, which is based on wavelets. This enables us to separate several aspects of a function and modify one selected exclusively. The quality of this approach is dependent on the choice of the wavelet decomposition. We demonstrate for Haar-wavelets how to estimate changes a priori and how to avoid modifications locally. A more general result is shown for all wavelet decompositions with finite filters. This knowledge can for example be used for a selective encrypting, where only a part of the data must be hidden. We implemented it using a wavelet decomposition, and found the described tools quite handy.