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FUSING SAR AND OPTICAL IMAGES BASED ON COMPLEX WAVELET TRANSFORM 
Shuai Xing*, Qing Xu 
Dept, of Remote Sensing Information Engineering, Institute of Surveying and Mapping, 450052 Longhai Middle Road, 
Zhengzhou City, China-xing972403@163.com 
Commission VII, WG VI 
KEY WORDS: Algorithms, Multiresolution analysis, Synthetic aperture radar, Image fusion, Multispectral, Remote sensing 
ABSTRACT: 
Image fusion deals with the integration of remote sensing images from various sensors, such as SAR and optical images, aiming at 
achieving improved image information to better support improved image classification, monitoring and etc. The main goal of this 
paper is to introduce an algorithm to fuse SAR and multi-spectral optical images based on complex wavelet. First, the theoretical 
basis of complex wavelet is described together with its key properties (e.g. approximate shift invariance, good directional selectivity, 
perfect reconstruction (PR),limited redundancy and efficient order-N computation). Secondly, the fusing algorithm based on complex 
wavelet is proposed, which includes a method to de-noise SAR image and a new fusion rule based on modulus of complex wavelet 
coefficients. Finally, experiment results show that the fusion method based on dual-tree complex wavelet transform (DT-CWT) is 
remarkably better than that based on discrete wavelet transform (DWT). 
1. INTRODUCTION 
SAR and optical remote sensing image fusion is aiming at 
achieving improved image quality to better support improved 
image classification, monitoring and etc. Fused image will 
enhance reliability and speed of feature extraction, increase the 
usage of the data sets, and extend remote sensing images’ 
application area. There have been a lot of research efforts on 
image fusion, and many fusion methods have been proposed. 
One of them, the fusion algorithm based on DWT, has been 
canonized. 
The advantages of wavelet are that it can analyze signal in time 
domain and frequency domain respectively and the 
multi-resolution analysis is similar with Human Vision System. 
DWT in maximally decimated form established by Mallat (S G 
Mallat, 1989) is widely used in image processing now, such as 
image matching, image segmentation, image classification, 
image fusion and so on. The best advantage of fusion based on 
DWT is to conserve more spectral characteristics of the 
multi-spectral image. So the fusion algorithm based on DWT is 
widely used. But DWT has two main disadvantages (N. 
Kingsbury, 1998a): 
• Lack of shift invariance. This means that small shifts in 
the input signal can cause major variations in the 
distribution of energy between wavelet coefficients at 
different scales. 
• Poor directional selectivity for diagonal features, because 
the wavelet features are separable and real. 
Nick Kingsbury has introduced the dual-Tree complex wavelet 
transform (DT-CWT), which has the following properties (N. 
Kingsbury, 1998a): 
• Approximate shift invariance; 
• Good directional selectivity in 2-dimensions (2-D) with 
Gabor-like filters also true for higher dimensionality: 
m-D); 
• Perfect reconstruction (PR) using short linear-phase 
filters; 
• Limited redundancy: independent of the number of scales: 
2:1 for 1-D (2 m : 1 for m-D); 
• Efficient order-N computation - only twice the simple 
DWT for 1-D (2 m times for m-D). 
DT-CWT has shown good performance in image restoration 
and denoising (A. Jalobeanu , 2000; Nick Kingsbury, 1998b; 
Peter de Rivaz, 2001), motion estimation (Julian Magarey, 
1998), image classification (Serkan Hatipoglu, 1999), texture 
analysis (Javier Portilla, 1999; N. Kingsbury, 1998; Serkan 
Hatipoglu, 1999), image enhancement (Nick Kingsbury, 
1998b), image matching (JIANG Han-ping , 2000). 
In this paper, we proposed an SAR and optical image fusion 
algorithm based on DT-CWT, and use a Radarsat-1 SAR image 
and a SPOT5 multi-spectral image to test the performance of 
our algorithm. 
2. THE DUAL-TREE COMPLEX WAVELET 
TRANSFORM 
It is well-known that the real biorthogonal wavelet transform 
can provide PR and no redundancy, but it is lack of shift variant. 
Then Kingsbury (Julian Magarey, 1998;N. Kingsbury, 1998a ; 
Nick Kingsbury, 1998b; Serkan Hatipoglu, 1999) has 
developed a dual-tree algorithm with a real biorthogonal 
transform, and an approximate shift invariance can be obtained 
by doubling the sampling rate at each scale, which is achieved 
by computing two parallel subsampled wavelet trees 
respectively. 
For one dimension signal, we can compute two parallel wavelet 
trees. There is one sample offset delay between two trees at 
level 1, which is achieved by doubling all the sample rates. The 
shift invariance is perfect at level 1, since the two trees are fully 
decimated. To get uniform intervals between two trees beyond 
level 1, there have to be half a sample delay. The term will be 
satisfied using odd-length and even-length filters alternatively 
from level to level in each tree. Because we use the decimated 
form of a real discrete wavelet transform beyond level 1, the 
shift invariance is approximate. 
The transform algorithm is described as following.