Lecture 26 Wavelet Transform
與FFT的差別
Fourier Transform:represents an array of pixel intensities in terms of pure frequency functions
Wavelet transform: expresses an image array in terms of functions which are restricted both in terms of frequency and spatial extent
基本上Wavelet transform 的定義是inner product 的一個概念 且associated function space
Definition
If f and g are two functions on the set of real number R, then their inner product is given by
Function space L2(R ) is the collection of all funcitons f:R->R with the property
Haar wavelet
Haar scaling function is the function
if 0≤x≤1
otherwise
We will use it to represent pixel intensities
Image compression
The fact that many of the wavelet coefficients area close to zero makes the wavelet transform useful for image compression.
Multiresolution analysis
Standard basic functions
These are functions which are zero everywhere outside a closed, bounded interval
Z is all integers
Orthornormal basis for
MRA
The dilation equation and refinement coefficients
The cascade algorithm: iterate the refinement coefficients for a scaling function, 可以近似到任何想要的精確度
The mother wavelet：與 Haar mother 近似
The Daubechies D4 scaling function比Haar更好用
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