Self-similarity is a key feature of both wavelets and fractals. In the first part of this talk we will review the definition of a multiresolution analysis (MRA) and examine the self-similarity of MRA wavelets by example of the Haar wavelet on the line and in the plane. We will use image compression as motivation in the two dimensional case.

The second part of the talk will show how we can combine the self-similarity of wavelets with the self-similarity of fractals by putting wavelets on enlarged fractal spaces using the construction of D. Dutkay and P. Jorgensen. The examples we will consider will be based on the middle-thirds Cantor set and Sierpinski's gasket. We will also perform image compression using a Sierpinski gasket fractal wavelet and compare it with our previous Haar example.

DE/Geom/Top Seminar main page