Wavelets: A New Tool in Applied Mathematics

The subject of wavelets has been around for less than ten years. Yet it seems to be popping up everywhere. The major reason for this is its usefulness in applications. Wavelets reduce the data requirements in fields such as image analysis and signal processing by their localization property: A function that is zero in an interval has a wavelet expansion whose partial sums are small or even zero. Since most of the information in an image or a signal is in the region where it changes, only the local data corresponding to it needs to be considered. Wavelets do this well, much better than classical methods.