Abstract-Since Chavez proposed the highpass filtering procedure to fuse multispectral and panchromatic images, several fusion methods have been developed based on the same principle: to extract from the panchromatic image spatial detail information to later inject it into the multispectral one. In this paper, we present new fusion alternatives based on the same concept, using the multiresolution wavelet decomposition to execute the detail extraction phase and the intensity-hue-saturation (IHS) and principal component analysis (PCA) procedures to inject the spatial detail of the panchromatic image into the multispectral one. The multiresolution wavelet decomposition has been performed using both decimated and undecimated algorithms and the resulting merged images compared both spectral and spatially. These fusion methods, as well as standard IHS-, PCA-, and wavelet-based methods have been used to merge Systeme Pour l'Observation de la Terre (SPOT) 4 XI and SPOT 4 M images with a ratio 4 : 1. We have estimated the validity of each fusion method by analyzing, visually and quantitatively, the quality of the resulting fused images. The methodological approaches proposed in this paper result in merged images with improved quality with respect to those obtained by standard IHS, PCA, and standard wavelet-based fusion methods. For both proposed fusion methods, better results are obtained when an undecimated algorithm is used to perform the multiresolution wavelet decomposition.Index Terms-Decimated wavelet transform, intensity-hue-saturation (IHS) transform, image-fusion, multiresolution analysis, principal component analysis (PCA), undecimated wavelet transform.

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Abstract. A Banach space X is said to be an M-space if every continuous multilinear form on X is weakly sequentially continuous. We study in this paper the stability properties of the class of M-spaces.2000 Mathematics Subject Classification. 46B20, 46B28, 46B08.

Abstract. We study the extension of bilinear and multilinear forms from a given subspace of a Banach space to the whole space. Precisely, an isomorphic embedding j : E → X is said to be (linearly) N -exact if N -linear forms on E can be (linear and continuously) extended to X through j. We present some necessary and sufficient conditions for j to be 2-exact, as well as several examples of 2-exact embeddings. We answer a problem of Zalduendo: in a cotype 2 space bilinear extendable and integral forms coincide.