Wavelet Local Extrema Applied to Image Processing

摘要

The research project had two components. In the first part, we developed anumerical method, based on the wavelet transform, for the solution of partial differential equations. Singularities and sharp transitions in solutions of partial differential equations model important physical phenomena, which are hard to simulate with conventional numerical methods. We introduced a numerical scheme based on the orthogonal wavelet transform, that adapts the computational resolution in space and time to the regularity of the solution. This scheme saves computations by concentrating the computational effort in regions where singularities or sharp transitions occur. It has been tested on the Burgers equation.