October 2015
Beginner
551 pages
17h 46m
English
Content preview from A Computational Introduction to Digital Image Processing, 2nd Edition
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436 A Computational Introduction to Digital Image Processing, Second Edition
15.2 A Simple Wavelet: The Haar Wavelet
The Haar wavelet has been around for a long time, and has been used with images as
the Haar transform. Only recently has the Haar transf orm been viewed as a simple wavelet
transform. In fact, the Haar wavelet is the simplest possible wavelet, and for that reason is
a good starting place.
The Haar wavelet is defined by the function
ψ(x) =
1 if 0 < x < 1/2
−1 if 1/2 ≤ x < 1
0 otherwise
and is shown in Figure 15.3. As with our wavelet function w(x), we can compress and
ψ(x) φ(x)
FIGURE 15.3: The Haar wavelet and pulse function
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