Attributes
Harr
Daubechies
BiorSplines
Coiflets
Symlets
Morlet
Orthogonality
Yes
Yes
No
Yes
Yes
Yes
The tighten
support length
1
2N-1
2N+1
6N-1
2N-1
00
Filter length
2
2N
2N+2
6N
2N
[-4,4]
Symmetry
Symmetry
Symmetry
approximatively
Asymmetry
Symmetry
approximatively
Symmetry
approximatively
No
Vanishing
moment
1
N
N-l
2N
2N
-
Table. 1 Attributes of the different wavelet bases
Form the table 1, the filter length of Haar wavelet is 2. The
filter length makes a great effect on the image fusion. The
shorter the filter length is, the more the target information loses.
In the case of the same filter length, the great vanishing
moment will lead to the smaller wavelet coefficients that may
be ignored under detailed scale, and makes the detail of the
image blurry. Symmetry can reconstruct the image well.
Therefore, Daubechies wavelet is chosen to integrate the SAR
and optical images in the paper.
3. DAUBECHIES WAVELET LIFTING TRANSFORM
expressed as:
fh(z) = h 0 + l\z 1 + h 2 z 2 + h i z 3
[ g(z) = -h^z 2 + h 2 z — 1\+ h 0 z~ ]
(l)
Where
/2 0 = (1 + v/3 ) / 4 V2,/tj = (3 + V3 ) / 4 v/2
h 2 = (3 - v/3 ) / 4, h 3 = (1 - V3 ) / 4V2
The wavelet lifting technique has widely been applied. The
lifting wavelet presents the under trait: calculating in the same
location, manifesting the high efficiency, calculating in the
parallel means, constructing easily and transforming by integer
[4 l Usually, the lifting wavelet may be constructed with two
kinds of the ways. On the one hand the traditional wavelet may
be implemented by the lifting scheme means, on the other hand
the new wavelet may directly be constructed using the lifting
means.
For the Daubechies D4, the function of the filter may be
To decompose the multiphase matrix, the under equation may
be obtained:
’i S'
1 0'
1 z
(V3+l)/V2 0
0 1
ß/4+(S-2)/4z-' 1
0 1
0 (V3-l)/V2_
(2)
Step
The transform forward
The transform backward
Step 1
s (0) = X
¿k A 2k
4 2) =Cd t
Step 2
d T = X 1M
4 2) = s t /(
Step 3
4™-d«»+«(,«■>+,{«)
4'>=^fw£)-4 2>
Step 4
sT=s^+ß(d^ + d^)
^ ,, = r(4 1, +4‘- , l )-4 2>
Step 5
4«>=A4 1, +^i)-4 1)
Step 6
4 0) =«(4 0) +4°-l)-4 1>
Step 7
* t = c4 2>
1 = 4 0)
Step 8
x u= st t >)
Table.2 The Lifting process of the Daubechies wavelet
