FUSION OF REMOTE SENSING IMAGE 
BASE ON THE PC A+ATROUS WAVELET TRANSFORM 
Yan Luo, Rong Liu, Yu Feng Zhu 
EAST CHINA INSTITUTE OF TECHINOLOGY 
Commission VI, WG VII/6 
KEYWORDS: Image fusion. High spatial resolution, wavelet decomposition, Assessment criteria, PC A 
ABSTRACT: 
On the basis that the PCA transformation and additive wavelet transformation have their own advantages and disadvantages 
higher spatial resolution can be acquired from the PCA transformation; however, more serious distortion of spectral 
characteristics can happen as well. While, the atrous wavelet transformation is able to preserve spatial information; however, the 
result is lack of high spatial resolution. A new technique, based on additive wavelet decomposition and PCA transformation was 
developed for the merging and data fusion of such images in this paper. Firstly we must get a fusion image by using the PCA 
transformation to merge the multispectral image and the high-resolution panchromatic image. Then we get the new principle 
components for the new multispecral image, while greatly parts of data information is included in the first component of the fused 
image. And then we apply the atrous wavelet merger to merge the multiresolution image and the first component of the fused image 
by PCA merger which substituted of the high-resolution panchromatic image. The new method is capable of preserving its spectral 
content while enhancing the spatial quality of the multispectral image to a greater extent. 
1 INTRODUCTION 
There are several situations that simultaneously require high 
spatial and high spectral resolution in a single image. This is 
particularly important in remote sensing. In other cases, such as 
astronomy, high spatial resolutions and high signal-to-noise ratio 
(SNR) may be required ^. However, in most cases, instruments 
are not capable of providing such data either by design or because 
of observational constraints. For example, in remote sensing, the 
SPOT satellite platform provides high-resolution (10m pixels) 
panchromatic data, while LANDSAT TM satellite data provides 
low-resolution (30m pixels) multispectral images. 
One possible solution comes from the field of data fusion. A 
number of methods have been proposed for merging panchromatic 
and multispectral data. The most common procedures are the 
Principal Component Analysis transform based methods (PCA 
mergers). However, the PCA methods produce spectral 
degradation. This is particularly crucial in remote sensing if the 
images to merge were not taken at the same time. In the last few 
years, multiresolution analysis has become one of the most 
promising methods for the analysis of images in remote sensing. 
Recently, several authors proposed a new approach to image 
merging that uses a multiresolution analysis procedure based upon 
the discrete two-dimensional (2-D) wavelet transform ’ . We 
also carried out a preliminary study of the wavelet-based method 
in combination with image reconstruction. Multiresolution 
analysis based on the wavelet theory permits the introduction of 
the concepts of details between successive levels of scale or 
resolution. Wavelet decomposition is increasingly being used for 
the processing of images. The wavelet approach preserves the 
spectral characteristics of the multispectral image better than the 
standard IHS methods. 
2 WAVELETS AND WAVELET TRANSFORM 
The method is based on the decomposition of the image into 
multiple channels based on their local frequency 
content wavelet transform can produce the images in 
different resolution. Wavelet represention refers to both 
spatial and frequency spaces. It can show a good position of a 
function (a.k.a image) in spatial and frequency space. The 
wavelet transform provides a framework to decompose 
images into a number of new images, each one of them with a 
different degree of resolution. While the Fourier transform 
gives an idea of the frequency content in our image, the 
wavelet representation is an intermediate representation 
between the Fourier and the spatial representation, and it can 
provide good localization in both frequency and space 
domains. There are different approaches to do wavelet 
decomposition. One of them is Mallat algorithm which uses 
wavelet functions such as Daubechies functions (db 1, 
db2 ,...). In this study we used the discrete wavelet transform 
algorithm known as atrous algorithm, (with holes) which used 
dyadic wavelet to merge nondyadic data in a simple and 
efficient procedure. In this algorithm a successive 
convolution using a filter was applied to the discrete wavelet 
transform. The wavelet transform of a distribution can be 
expressed as ^ : 
(II-UI) 
W’ „’o’ „’ 
16 4 8 4 16 
"Vi6" 
'1 4 6 4 1' 
i/4 
1 
~ 256 
4 16 24 16 4 
2/8 
6 24 36 24 6 
1/4 
4 16 24 16 4 
m 
1 4 6 4 1 
-To use convolution function directly. 
In each step we get a new version of the image I u I 2 , The 
wavelet coefficient is defined as follows: