A FUSION ALGORITHM OF HIGH SPATIAL AND SPECTRAL RESOLUTION IMAGES 
BASED ON ICA 
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, 
136000; 
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 
Abstract 
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. 
1. INTRODUCTION 
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. 
2. ICA AND FAST ALGORITHMS 
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: 
n 
v. =a,s, +a.,s, h b as = >as. 
i il l 12 2 13 3 in n / ii.ii 
7=1 
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‘ 
i 
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) = - 
c 
G 2 {y) = - 
*a:E-mail:ldxyzgk@163.com;phone(+86-0434)3291780 
*c Corresponding author: E-mail:zhy@nenu.edu.cn;phone+8613074334258