Digital Signal Processing Reference
In-Depth Information
% Compute CWT with Mexican hat wavelet.
cwt = CWT(x,nvoice,WaveName,octave,4);
% display CWT
subplot(212);
ImageCWT(fliplr(cwt),'Individual','gray','log',octave,4);
set(gca,'FontSize',14);
xlabel('Position');ylabel('log_2(scale)');title('CWT')
2.9.3 Nonlinear Approximation by Discrete Wavelet Transform
The goal of this code is to illustrate the properties of the DWT (here with the
7
9 biorthogonal pair) for approximating an image from its
m
best - largest in
magnitude - coefficients. It is well established that the nonlinear approximation
error decays like
m
−
α
, where
/
α
depends on the regularity of the image. For example,
bounded variation images and piecewise regular images have a nonlinear approx-
imation from their wavelet coefficients that exhibits a decay rate
m
−
1
(Cohen et al.
1999). This is, for instance, the case for “Lena,” as can be seen from Fig. 2.16(b).
(a)
(b)
28
26
24
22
20
4
6
8
10
12
14
log
2
(Number of retained DWT coeff)
(c)
(d)
Figure 2.16. (a) Original “Lena” image. (b) Best
m
-term nonlinear approximation
error. (c) Ten percent largest DWT coefficients. (d) Reconstruction from these 10
percent largest DWT coefficients; relative error, 0.0503.
