Wavelet Sets in Multiple Dimensions

By Krista Rister

The study of wavelets, a relatively new area of mathematics, is useful in signal processing. However, wavelets are for the most part complex and hard to understand. Wavelet sets, on the other hand, are easier to comprehend, and they can also be used to generate wavelets using the inverse Fourier transform. Thus, wavelet sets have become a valuable tool in the study of wavelets. Wavelet sets in higher dimensions are particularly interesting because their graphical representations make them somewhat easier to understand. Although wavelet sets exist in any arbitrary dimension, two- and three-dimensional wavelet sets are the concentration of my research. Rules for constructing wavelet sets will be shared, as well as examples of wavelet sets.