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^kpsi(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
• Matlab: wavelets1dimdwt.m
• Graphical user interface for compression and denoising.
• 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) h1 phi(2t-k).
• Discussion wavelet spaces: (Chapter 2 of Wavelets: Software and Applications by Geert Uytterhoeven Katholieke Universiteit Leuven, PhD Thesis, 1999.)

• Signals:
• leleccum.mat
• Images:
• woman.mat
• wbarb.mat
• detfingr.mat
• Matlab scripts:
• impulseresponse.m
• wavelets1dimdwt.m
• wavelets1dimmultilevel.m

---

Objective: Become familiar with wavelet composition calculations

---

Last revision: October 23, 2001 at 11:40 am