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Mapping without the sun
Zhang, Jixian

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
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).
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
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:
• Perfect reconstruction (PR) using short linear-phase
• 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.
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
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.