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Mapping without the sun
Zhang, Jixian

GuoKun Zhang* 3 LeiGuang Wang b Hongyan Zhang* c
( a The Faculty of Tourism and Geographical Science ,Jilin Normal University, 1301 Haifeng Street,Siping, Jilin Province, China,
b National Laboratory for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, 129 Luoyu
Road, Wuhan, China, 430079;
c .College of Urban and Environmental Sciences, Northeast Normal University, Renmin Dajie No. 5268,Changchun, China, 130024)
Key words: ICA Transform, image fusion, multiresolution analysis
Independent component analysis (ICA) is a recently developed linear data analysis method. By using ICA method, the correlation
and redundancy of multispectral images can be eliminated. In detail, our algorithm can be divided into the following steps (as shown
in figure 1).Firstly, ICA transform is operated on MS imagery, and then, we get three new independent bands. Secondly, the shift-
invariant discrete wavelet transform (SIDWT) is used to PAN image. Then, the rule for combining the ICA coefficients in during
corresponding planes of the different plane is determined. Finally, inverse ICA is used to get the pan-sharpened image. Compared to
other algorithms of RS imagery fusion, our method reduces the data redundancy among MS image bands and also preserves the
spectral fidelity of the MS imagery as methods based on wavelet. Experiment result shows that our method can avoid the artifacts in
the fused images. Also, make higher performance in signal-to-noise ratio than an algorithm based on wavelet.
The goal fusing multispectral (MS) low-resolution remotely
sensed images with a more highly resolved panchromatic (PAN)
image is to obtain a high-resolution multispectral image which
combines the spectral characteristic of the low-resolution data
with the spatial resolution of the panchromatic image.[l]
Literature has shown a large collection of fusion methods
developed over the last two decades. Methods can be classified
into several strategies. The first is methods based on component
substitution, such as intensity-hue-saturation (IHS)[1],
principal component substitution (PCS) and Brovey method.
Although those are enhancing spatial resolution which are
suitable for tasks of human interpretation, the original
multispectral content of the image is greatly distorted. So fused
image may not be available for undertaking quantitative
analysis such as classification. Then, another family of methods
is developed later trying to overcome this limitation. That is
multi-resolution analysis (MRA), such as Laplacian pyramid
(LP) transform, discrete wavelet transform (DWT), etc.
Nowadays, the wavelet-based scheme for the fusion of
multispectral and panchromatic imagery has become quite
popular due to its ability to preserve the spectral fidelity of the
MS imagery while improving its spatial quality. But not all
kinds of wavelet transform are available for fusion problem.
Some shift variance of the transform can lead to artifacts in the
fused images. In order to avoid this problem, a novel fusion
algorithm combined Independent component analysis (ICA)
and AtroUS wavelet was proposed in this paper. The rest part
is arranged as follows: in part two, the concept of ICA and a
first algorithm are introduced. In the third part, a novel high
frequency injection model in ICA domain is proposed. Finally,
the experiment result is analyzed in the part 4.
Independent component analysis (ICA) is a statistical method
for transforming an observed multidimensional random vector
into components that are statistically as independent from each
other as possible, which is proposed by Jutten and Herault in
1991 [2, 3]. The implication for feature extraction in remote
sensing has been found in many works[4].In the simplest way
[5], the ICA model can be described as follows: there are Yl
unknown statistically independent components
Sj, S 2 , S 3 , S 4 , • • • S n , and theirs linear combinations with YU
scalar variables Vj, V 2 , V 3 • • • V can be observed. That is:
v. =a,s, +a.,s, h b as = >as.
i il l 12 2 13 3 in n / ii.ii
i = 1,2,3 ••• m
Generally speaking, Yl is not larger than m. if so, principle
component analysis is used to reduce dimension from YYl to
Yl .Then, if we arrange both the observed variables V- and the
component variables S t into vectors respectively, a matrix form
of (1) can be given by
V = As (2)
Where,V = (v l ,V 2 ,V 3 ---V m ) T ,S = (S 1 ,S 2 ,S 3 ---S„) T *
nd A is an unknown constant matrix, which is called the mix
matrix. Then we can define a demixing matrix W, which can be
given by:
y = Wv
Our target is to es
all observed sign
optimum estimate
estimate of variab
Because a linear
Gaussian variable,
be allowed to be a
In detail, the algi
preprocessing step
order to remove t
data dimension (i
L(W) using the
measure the inde
optimization algoi
W ,which make
equal to W . The
combination of
algorithm[7]. The
statistical impend
objective functior
minimum of mutus
been improved thi
the term of inforrr
is laying in the o
calculating comp]
negentropy are ol
random variable )
as follows:
kurt(y) = e{
Meanwhile, its ne
difference betweer
same as y in star
H(x) = ~Z‘
Yie(y) = H(y
A large collection
been proposed in
robust ICA (Fast-F
widely used, whi<
minimum of neger
using (6) as a critc
into function (7) in
My) = [E
y = w
In which, V is a
variance and y is
Function G(») ca
Two commonly us<
G i(y) = -
G 2 {y) = -
*c Corresponding author: E-mail:zhy@nenu.edu.cn;phone+8613074334258