CS 6723 Image Processing
Lecture 17: Wavelets (Continued)
- Example of 1-dimensional wavelet decomposition
- Matlab: wavelets1dimdwt.m
- Vanishing moments (order n) if average of x^{k}psi(x) for k = 0..n. This
implies that the wavelet can remove nth order polynomials
- Regularity: related to how how differentiable the wavelets are.
- Example of multilevel 1-dimensional wavelet decomposition
- Wavelet packet analysis:
- Full tree analysis.
- Graphical user interface.
- Wavelets in 2Dim
- Wavelet scaling equation
- Dilation equation:
phi(t) = 2 * sum(k = 0 to N) h(k) phi(2t-k)
- Require integral of
phi(t)
to be 1.
- Wavelet equation:
w(t) = 2 sum(k=0 to N) h_{1} phi(2t-k)
.
- Discussion wavelet spaces:
(Chapter 2 of Wavelets: Software and Applications by Geert Uytterhoeven
Katholieke Universiteit Leuven, PhD Thesis, 1999.)
- Signals:
- Images:
- Matlab scripts:
Objective: Become familiar with wavelet composition calculations
Last revision: October 23, 2001 at 11:40 am