Constructions of Orthogonal and Biorthogonal Scaling Functions and Multiwavelets Using Fractal Interpolation Surfaces

Bruce Kessler, Western Kentucky University

Abstract

This chapter is a survey of the work that has been done by Donovan, Geronimo, Hardin, and the author in constructing orthogonal scaling vectors and multiwavelets, and by the author in constructing biorthogonal scaling vectors and multiwavelets, using fractal interpolation surfaces. Scaling function coefficients for all of the constructions are provided in the appendix. Image compression and denoising examples using the orthogonal bases are provided.