Department van Wiskundige Wetenskappe

Wiskunde

Wavelet and Subdivision Analysis

Techniques based on wavelets and subdivision have developed over the last two decades into powerful tools in the application areas of, respectively, signal analysis and computer-aided design (CAD). Underlying the mathematical foundations of both wavelets and subdivision is the concept of a refinable function, i.e. a finitely-supported continuous function with the self-reproducing property of being expressible as a finite linear combination of the integer shifts of its own contraction by factor 2. The Wavelet Research Group under the leadership of Prof Johan de Villiers consisting of a group of 10 research students and other academics, has as its focus specifically the mathematical analysis of wavelets and subdivision.

Since the field is relatively new, there exists a multitude of open questions in the mathematical theory of wavelets and subdivision, in particular with respect to the existence, construction and properties of refinable functions in both the scalar and vector cases. Members of the group who recently obtained PhD degrees are: Karin Hunter (2005), Desiree Moubandjo (2007), Deter de Wet (2007), Blaise Dongmo (2007) now working at Koeberg.

Some references for further reading include:

  1. C.K. Chui. Introduction to Wavelet Analysis. Academic Press, 1992.
  2. I. Daubechies. Ten Lectures on Wavelets, SIAM, 1992.
  3. C.A. Micchelli. Mathematical Aspects of Geometric Modeling. SIAM, 1995.

For more information please contact Prof. J. de Villiers.