Multi-Band Wavelet for Fusing SPOT Panchromatic and Multispectral Images

With the development of remote sensing technology, fusion of remotely sensed images, such as SPOT panchromatic (SPOT P) with SPOT multispectral images (SPOT XS) or Landsat Thematic Mapper (TM), has become more important in order to obtain richer information in the spatial and spectral domains simultaneously. Many fusion methods have been developed based on the two-band wavelet transformation. However, due to the limitations of the transformation characteristics themselves, the two-band wavelet is not very efficient for the fusion of images whose ratio of spatial resolutions is not 2n (n 1, 2, 3, ...), e.g., for fusing a 10-m resolution panchromatic SPOT image and with 30-m resolution multispectral TM images. However, a recently developed new wavelet branch—multi-band wavelet—can potentially be applied to solve this problem. In this paper, we develop a new approach for fusing SPOT P images with multispectral TM images based on multi-band wavelet transformation. First, the theoretical basis of multi-band wavelet is presented and its transformation properties are analyzed. Second, a new method for fusing a SPOT P image with multispectral images using the multi-band wavelet is proposed. Specifically, the threeband wavelet is implemented to fuse 10-m SPOT panchromatic and 30-m multispectral TM images. Third, this new method is compared with previous methods such as the two-band wavelet and IHS methods for image fusion. The proposed multi-band wavelet approach demonstrates an improvement in spatial and spectral characteristics for fusing SPOT P and multispectral TM images. Introduction With the development of remote sensing technology, various remotely sensed imageries—multiand high-spectrum, multiangle viewing, and multi-resolution—have been provided. These include one-meter resolution images such as Ikonos, large frame images, multispectral TM images, panchromatic and multispectral SPOT images, InSAR data, and many others. Each of these images has its own characteristics and contains certain types of information which may be superior spectrally or spatially. It is essential to develop advanced image fusion technologies, so that the advantages of the different remote sensing images can be integrated and to generate images with rich spatial and spectral information simultaneously. Such fused images will provide more detailed and accurate information, and can thus extend the areas of application, improve the reliability of their use, and increase the speed of information and feature extraction. Therefore, image fusion is an important technique to be developed, particularly when multi-sources of remote sensing images are available. There have been many research efforts on image fusion (Carper et al., 1990; Ehler, 1991; Wald, 1999; Nunez et al., 1999; Zhang, 1999). These methods can be divided into three categories: (1) pixel-based image fusion, (2) feature-based fusion, and (3) recognition (interpretation)-based fusion. Many of these methods have been widely used, for example, pixelbased weighted image fusion, the IHS color model, the PCA method, the HLS fusion method, the COS fusion method, and the HSV (Hue, Saturation, and Value) method (Li et al.; 1998; Yang et al., 1988; Carper et al., 1990; Shettigara, 1992; Zhang, 1999). 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 evaluating the spectral quality of the fused satellite images. One of the objectives of image fusion is to construct synthetic images that are closer to the reality they represent. According to the criteria proposed by Wald et al. (1997), the Brovey, IHS, and PCA fusion methods meet this objective (Ranchin and Wald, 2000). However, one limitation of such methods is some distortion of spectral characteristics in the original multispectral images. Fused images with such distortions may cause difficulties for further use of the image in interpretation and image analysis. Recent developments in wavelet analysis provide a potential solution to these drawbacks. For example, Bruno et al. (1996) employed two different tools originally from signal processing: multi-resolution analysis and the two-band wavelet transformation. Sun et al. (1998) studied the fusion of remote sensing data based on two-band wavelet features. Nunez et al.(1999) developed an approach to fuse a highresolution panchromatic image with a low-resolution multispectral image based on wavelet decomposition. Ranchin and Wald (2000) designed the ARSIS concept for fusing high spatial and spectral resolution images based on the multiresolution analysis of two-band wavelet transformation. Similar studies were conducted by Yocky (1995), Ranchin et al. (1996), Zhou et al. (1998), Blanc et al. (1998), and Li et al. (1999). However, all of these developments were based on the two-band wavelet transformation. Using the two-band wavelet transformation, an image can be decomposed into a low-frequency portion and three high-frequency portions. For example, Figure 1 is a twoband wavelet decomposition of the Lenna image. P H O T O G R A M M E T R I C E N G I N E E R I N G & R E M O T E S E N S I N G May 2003 513 Photogrammetric Engineering & Remote Sensing Vol. 69, No. 5, May 2003, pp. 513–520. 0099-1112/02/6905–513$3.00/0 © 2003 American Society for Photogrammetry and Remote Sensing W.Z. Shi is with the Advanced Research Centre for Spatial Information Technology, Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong ([email protected]). C.Q. Zhu and C.Y. Zhu are with ZhengZhou Institute of Surveying and Mapping, ZhengZhou, 450052, China ([email protected]). X.M. Yang is with the State Key Lab., Resources and Environment Information System, Chinese Academy of Science, 100101, Beijing, China. We know that the ratio of the spatial resolutions of the two images to be fused can be one of the following two cases: (I) 2n (n 1, 2, 3, ...), such as two, four, eight, sixteen, etc., and (II) others, such as three, five, six, etc. The two-band wavelet transformation, due to its decomposition characteristics, can be directly applied for images with the type (I) spatial resolution relationship. For example, one may fuse an image with 10-m resolution (e.g., SPOT P) with an image of 20-m resolution (e.g., SPOT XS) using a two-band wavelet transformation, where the ratio of spatial resolution is 2. The basic ideal of the two-band wavelet transformation, for a type (I) case, is to replace the lowfrequency portion of the transformed image with a lowresolution image. These types of studies can be found, for example, in Ranchin and Wald (2000), where the authors fused images with spatial resolutions of 10 m, 20 m, and 40 m, respectively. The core of these applications is to make use of the transformation characteristics of the two-band wavelet. For an image fusion case with a type (II) relationship, the two-band wavelet cannot be applied directly. The images need to be pre-processed first, then transformed using the two-band wavelet. In such a case, a low-resolution image (e.g., a 30-m multispectral TM image) is scaled to be the same size or half size (in length and width) as the highresolution image (e.g., a 10-m panchromatic SPOT image) by a resampling processing, for example. However, the spectral information may be lost during such a resampling preprocess (Li et al., 1999). Therefore, it is not very efficient to apply the two-band wavelet transformation to fuse images with a type (II) relationship, for example, to fuse images with resolutions of 10 m and 30 m. A potential new solution for fusing images with type (II) relationships will be based on the multi-band wavelet – a new branch of the wavelet, and this is identified as the focus of this study which aims to improve the image fusion effects. The multi-band wavelet transformation has been studied in recent years. A multi-band wavelet transformation is superior to the two-band in many aspects, such as compact support and symmetry, especially in its decomposition characteristics. Now, both theoretical research (Chui et al. 1995; Bi et al., 1999; Wisutmethangoon et al., 1999) and a few application studies (Zhu, 1998; Zhu et al. 2002) have been performed with the multi-band wavelet. In the following section, the basic characteristics of the multi-band wavelet will be further introduced. It will be found, in this study, that the multi-band wavelet is very appropriate for fusing images with the type (II) relationships, i.e., where the ratio of the spatial resolution between two images is not 2n (n 1, 2, 3, ...). In this paper, we aim to propose a generic image fusion method based on the multi-band wavelet, where the ratio of spatial resolution of the images is not restricted to be 2n but to any integer number. A specific discussion of fusing SPOT P with multispectral TM images is taken as an example. The structure of this paper is as follows. The next section discusses the theoretical basis and transformation characteristics of the multi-band wavelet, and makes a comparison between the two-band wavelet and the multi-band wavelet. Then, a new image fusion approach for SPOT P and multispectral images based on the multi-band wavelet is presented. This is followed by a discussion of the image fusing experiments, including the three-band wavelet fusion of 10-m SPOT panchromatic and 30-m multispectral TM images. Next, the experimental results are analyzed. Furthermore, the proposed method is compared with the previous methods developed for image fusion, such as the two-band wavelet method and the IHS method. Characteristics of the Two-Band and Multi-Band Wavelet Transformations The Two-Band Wavelet Transformation Multi-Scale Analysis Wavelets are functions in a space , determined from a basic wavelet function by dilations and translations. They are used for representing the local frequency content of functions. The basic wavelet should be L(R) ef(x) ƒ