A Fusion Approach of Multi-sensor Remote Sensing Data Based on Wavelet Transform
He Guojin Li Kelu Hu Deyong
China Remote Sensing Satellite Ground Station, Beijing 100086
E-mail: gjhe@nts.rsgs.ac.cn
Abstract
The fusion of multisensor and multire solution satellite data is an effective means of exploiting the complimentary nature of different daya types. This paper presents a data fusion approach based on wavelet transform. With this kind of merger, higher spatial resolution SPOT-PAN data is fused with lower resolution multispectral TM. First of all, the paper makes a discussion on the effort of different length of Daubechies Wavelet Basis to the fused images, and then the wavelet approach as been compared to HIS and PCA image fusion technique and has been shown to possess the advantage of minimal distortion of the spectral characteristic of the data visible enhancement of spatial quality. It has exhibited the potential application of wavelet transform for higher accuracy for fusing spectral -spectral information of multisource sebsed data.
Introduction
A number of earth observation available satellite programs have provided us with huge remote sensing data in multi-sensor, multi-resolution, multi-spectral and multi-temporal. These data have built up a pyramied of image data for the investigation of global change, environment and limitations of these kinds of remote sensing data when they are applied to different research or practical purposes. That means, thus far, it has not been possible to propose a single sensor package that will meet all our application requirement, while the combined image from multiple sensors will provide more comprehensive information by collecting a wide diversity of sensed wavelengths, spatial resolutions, and look-angles. For that, greater emphasis today is being placing on the data fusion technique, an effective means of exploiting the complimentary nature of various imagery types, to generate an interpretation of the scene not obtainable with data from a single sensor, or to reduce the uncertainty associated with the data from individual sensor.
Many works have recongnized the benefit of merging multisensor and multiresolution satellite data, and numerous merging approaches, such as the HIS transform (Hayden it al. 1982), PCA analysis (Chavez, et al. 1991) and HPF method (Jim, 1996), were presented in previous literature. Recently, the wavelet transform has been used for merging data derived From different resolution sensors (Li et al. 1995, Yocky, 1996). However work has seldom been done to explore the effects of different wavelet coefficients to the fused image in both spectral and spatial features.
Aimed at geological application, this paper tries to merge the high-resolution SPOT PAN with the color TM images using wavelet transform. On the one hand, the authors perform a discuss on the relationship between wavelet coefficients and the fused results, and set up the fusion model called "FWT"; On the other hand, the paper also present a comparison of the fused images which were merged by wavelet transform, PCA and HIS methods respectively.
Review of the Wavelet Transform
If there exists a function
y(t), which is well localized and also meets the condition of:
we call that function group {
ya,b} generated by
y(t) is Analyzing Wavelet (Mallat 1989, mayer 1992):
Parameters: a is a scale factor and b is a translation factor
It has been proved that such a set of function
y(t)can generate a following orthogonal base of square bounded function L
2(R) by changing the a b parameters:
y (2
-k t-n) k,n denote the set of integers
Thus, each signal f(t) can be decomposed in the basis as followed, and the corresponding coefficients are defined as wavelet coefficients:
As for remote sensing data, we used a filtering approach of wavelet decomposition followed by subsampling (Mallat 1989). This is decomposed into a low pass approximation and three high pass detail images (wavelet coefficients) which correspond to the three direction : horizontal, vertical, and diagonal.
In that way four under images (HH, GH, HG, and GG) can be obtained from one full resolution image (Bruno Garguet-Duport et al. 1996). HH is the context image at the inferior resolution (the approximation), GH is the image of the horizontal details, HG is the image of the vertical details, and GG is the image of the horizontal details, HG is the image of the vertical details and GG is the image of the diagonal details(see Figure 1).
Perfect reconstruction of the original can also be achieved through the inverse wavelet transform (Daubechies, 1988).
Figure 1 One Level Diagram of Wavelet Transform
