The Use of Multiresolution Analysis and Wavelets Transform for Merging SPOT Panchromatic and Multispectral Image Data Bruno Garguet-Duport, Jacky Girel, Jean-Marc Chassery, and Guy Pautou Abstract Several techniques have been developed to merge SPOT 10-m resolution panchromatic data (SPOT P) with simultaneously ac- quired 20-m resolution multispectral data (SPOT XS). Normally, the objective of these procedures is to create a composite im- age of enhanced interpretability. The current merging methods may not be satisfying; they can distort the spectral character- istics of the xs images and, as a result, the analysis becomes difficult. In this paper a method allowing the use of 10-m res- olution xs data while conserving the spectral properties of the original 20-m data is presented. This method uses a multire- solution analysis procedure based upon the wavelets trans- form; it is applied to remotely sensed SPOT P and SPOT XS im- ages of the river junction Arc-Is&re (France). This new method is compared with the IHS method and P+XS method. The wavelets method is the one which least distorts the spectral characteristics of the data. The distortions are minjmal and difficult to detect. Introduction The objective of the improved image merging method is to generate hybrid high resolution multispectral images that at- tempt to preserve the radiometric characteristics of the origi- nal multispectral data. This is very important for our group because we are mostly interested in vegetation analysis. A number of methods for merging panchromatic images with multispectral images are known from literature. Pradi- nes (1986) proposed a method for merging four SPOT pan- chromatic pixels with a corresponding SPOT XS pixel. Price (1987) used merging methods for display techniques. Three merging methods have been compared (Chavez et al., 1991) and no example was found to be well adapted to vegetation analysis. The most common procedure was the Intensity- Hue-Saturation (IHS) method which has been used by Carper et al. (1990), Chavez et al. (1991), and Ehlers (1991). For ex- ample, recently Pellemans et al. (1993) have demonstrated B. Garguet-Duport is with the Centre de Biologie Alpine, La- boratoire Hydrosysthmes Alpins, BP 53 38041, Grenoble cedex 9, and TIMC-IMAG Institut Albert Bonniot Domaine de la Merci 38706 La Tronche Cedex. J. Girel is with the Centre de Biologie Alpine, Laboratoire Hydrosyst&mes Alpins, BP 53 38041, Grenoble cedex 9, and CNRS URA 1451, Ecologie des eaux douces et des grands fleuves (Lyon I). J.-M. Chassery is with the TIMC-IMAG Institut Albert Bon- niot Domaine de la Merci 38706 La Tronche Cedex. G. Pautou is with the Centre de Biologie Alpine, Laboratoire Hydrosysthmes Alpins, BP 53 38041, Grenoble cedex 9. that the IHS method was not adapted to vegetation, and they proposed a method based on the sensors radiometric proper- ties. It is desirable that any procedure for merging high reso- lution panchromatic data with low resolution multispectral data should preserve the original spectral characteristics of the latter as much as possible. The procedure should be opti- mal in the sense that only the additional spatial information available in higher resolution data is imported into the mul- tispectral bands. The purpose of the present study was to present a 10-m simulated method for xs images while conserving spectral properties of original XS 20-m images. This method uses two tools coming from the signal processing field, based on solid mathematical procedures: multiresolution analysis and the wavelet transform. This new merging method was compared with the most common merging procedures such as IHS (Carper et al., 1990; Kay, 1990) and P+xS (Anonymous, 1986). Multiresolution Analysis and Wavelet Transform The Wavelet Transform Multiresolution analysis based on wavelets theory permits the introduction of the concept of details between successive levels of scale or resolution. To define the wavelet transform (Meyer, 1992), it is nec- essary to introduce a function T(t) called the generating wavelet. Such a function T(t) is mainly concentrated near 0 and is characterized by a rapid decrease when I t I increases. We say that q t ) is well localized (Mallat, 1989). Moreover, qt) has to be oscillant in order to present a good localiza- tion in the frequency domain. This condition was expressed by the equation The generating wavelet allowed the introduction of wavelet !P(o,b) (t) depending on two parameters: a scale factor a and a translation factor b: i.e.. Grossmann and Morlet have proved that, under this condi- Photogrammetric Engineering & Remote Sensing, Vol. 62, No. 9, September 1996, pp. 1057-1066. 0099-1112/96/6209-1057$3.00/0 O 1996 American Society for Photogrammetry and Remote Sensing PE&RS September 1996 1057