Digital Signal Processing Reference
In-Depth Information
c
2
w
3/2
w
2
Wavelet coefficients
w
1/2
Wavelet coefficients
w
1
Figure 2.8. Feauveau's wavelet transform repre-
sentation of an image.
of the Feauveau quincunx decomposition algorithm. Figure 2.11 exemplifies such a
wavelet transform on the “Lena” image.
In Van De Ville et al. (2005), the authors introduced new semiorthogonal 2-D
wavelet bases for the quincunx subsampling scheme. But unlike the traditional de-
sign, which is based on the McClellan transform, those authors exploited the scaling
relations of the 2-D isotropic polyharmonic B-splines.
a
fbf
jgcgc
fgidigf
abcdedcba
fgidigf
jgcgc
fbf
a
h
h
a
0.001671
-
b
−
0.002108
−
0.005704
c
−
0.019555
−
0.007192
d
0.139756
0.164931
e
0.687859
0.586315
f
0.006687
-
g
−
0.006324
−
0.017113
0.014385
j 0.010030 -
Figure 2.9. Coefficients of the nonseparable 2-D low-pass filter
h
and its dual
h
used in
Feauveau wavelet transform.
i
−
0.052486
−
