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THE CURVELET TRANSFORM FOR IMAGE FUSION 
Myungjin Choi * , Rae Young Kim" *, Moon-Gyu Kim" 
* SaTReC, " Division of Applied Mathematics , KAIST 
373-1, Guseong-dong, Yuseong-gu, Daejeon, 305-701, Republic of KOREA 
* (prime,mgkim)@satrec.kaist.ac.kr; ° rykim@amath.kaist.ac.kr 
KEY WORDS: Fusion, Multiresolution analysis, IKONOS, Wavelet transform, Curvelet transform 
ABSTRACT: 
The fusion of high-spectral but low spatial resolution multispectral and low-spectral but high spatial resolution panchromatic 
satellite images is a very useful technique in various applications of remote sensing. Recently, some studies showed that wavelet- 
based image fusion method provides high quality of the spectral content of the fused image. However, most of wavelet-based 
methods have a spatial resolution of the fused result less than the Brovey, IHS, and PCA fusion methods. In this paper, we 
introduce a new method based on the curvelet transform which represents edges better than wavelets. Since edges play a 
fundamental role in image understanding, one good way to enhance spatial resolution is to enhance the edges. Curvelet-based image 
fusion method provides richer information in the spatial and spectral domains simultaneously. We performed IKONOS image fusion. 
This new method has reached an optimum fusion result. 
1. INTRODUCTION 
In many remote sensing and mapping applications, the fusion 
of multispectral and panchromatic images is a very important 
issue. 
Many image fusion techniques and software tools have been 
developed. The well-known methods are, for example, the 
Brovey, the IHS(Intensity, Hue, Saturation) color model, the 
PCA(Principal Components Analysis) method, and wavelet 
based method(Ranchin er a/.2000). 
Assessment of the quality of the fused images is another 
important issue. Wald et al. (1997) proposed an approach with 
criteria that can be used for evaluation the spectral quality of 
the fused satellite images. 
If the objective of image fusion is to construct synthetic images 
that are closer to the reality they represent, then, according to 
the criteria proposed by Wald et al.(1997)., the Brovey, IHS, 
and PCA fusion methods meet this objective. However, one 
limitation of such methods is some distortion of spectral 
characteristics in the original multispectral images. Recently 
developments in wavelet analysis provide a potential solution 
to these drawbacks. For example, Nunez et al.(1999) developed 
an approach to fuse a high-resolution panchromatic image with 
a low-resolution multispectral image based on wavelet 
decomposition. Ranchin and Wald designed the ARSIS concept 
for fusing high spatial and spectral resolution images based on 
the multiresolution analysis of two-band wavelet transformation. 
Wavelet-based image fusion method provides high spectral 
quality of the fused satellite images. However, the fused image 
by Wavelets have much less spatial information than those by 
the Brovey, IHS, and PCA methods. The spatial information of 
fused image is an important factor as much as the spectral 
information in many remote sensing applications. In particular, 
this improves the efficiency of the image fusion application, 
  
* The second author was supported by KRF-2002-070-C00004. 
59 
such as unsupervised image classification. In other words, it is 
necessary to develop advanced image fusion method so that the 
fused images have the same spectral resolution as the 
multispectral images and the same spatial resolution as the 
panchromatic image with minimum artifacts. 
Recently, other multiscale systems have been developed, which 
include in particular ridgelets (Candes, 1999) and curvelets 
( Candes et al, 1999;Starck et al,2002), and these are very 
different from wavelet-like systems. Curvelets and ridgelets 
take the form of basis elements which exhibit very high 
directional sensitivity and are highly anisotropic. Therefore, 
the curvelet transform represents edges better than wavelets, 
and is well-suited for multiscale edge enhancement(Starck et 
al,2002). 
In this paper, we introduce a new image fusion method based 
on the curvelet transform. The fused image using curvelet-based 
image fusion method represents almost the same detail as the 
original panchromatic image because curvelets represent edges 
better than wavelets, and the same colour as the original 
multispectral images because we use the wavelet-based image 
fusion method naturally in our algorithm. Therefore, this new 
method is an optimum method for image fusion. We develop a 
new approach for fusing IKONOS pan and multispectral images 
based on the curvelet transform. 
The structure of this paper is as follows. The next section 
describes the theoretical basis of the ridgelets and curvelets. 
Then, a new image fusion approach for IKONOS pan and 
multispectral images based on the curvelet transform is 
presented. This is followed by a discussion of the image fusing 
experiments. Next, the experimental results are analysed. 
Furthermore, the proposed method is compare with the previous 
methods developed for image fusion, such as the wavelet 
method and the IHS method.