Balanced biorthogonal scaling vectors using fractal function macroelements on |
| |
Authors: | Bruce Kessler |
| |
Institution: | aDepartment of Mathematics, Western Kentucky University, 1906 College Heights Blvd., Bowling Green, KY 42101, USA |
| |
Abstract: | Geronimo, Hardin et al. have previously constructed orthogonal and biorthogonal scaling vectors by extending a spline scaling vector with functions supported on 0,1]. Many of these constructions occurred before the concept of balanced scaling vectors was introduced. This paper will show that adding functions on 0,1] is insufficient for extending spline scaling vectors to scaling vectors that are both orthogonal and balanced. We are able, however, to use this technique to extend spline scaling vectors to balanced, biorthogonal scaling vectors, and we provide two large classes of this type of scaling vector, with approximation order two and three, respectively, with two specific constructions with desirable properties in each case. The constructions will use macroelements supported on 0,1], some of which will be fractal functions. |
| |
Keywords: | Biorthogonal Balanced Fractal functions Macroelements Multiresolution analyses Multiwavelets Orthogonal Scaling vectors Wavelets |
本文献已被 ScienceDirect 等数据库收录! |
|