We propose an algorithm to increase the resolution of multispectral satellite images knowing the panchromatic image at high resolution and the spectral channels at lower resolution. Our algorithm is based on the assumption that, to a large extent, the geometry of the spectral channels is contained in the topographic map of its panchromatic image. This assumption, together with the relation relating the panchromatic image to the spectral channels, and the expression of the low resolution pixel in terms of the high resolution pixels given by some convolution kernel followed by subsampling, constitute the elements to construct an energy functional (with several variants) whose minima will give the reconstructed spectral images at higher resolution. We shall discuss the well foundedness of the above approach and describe our numerical approach. Finally, some experiments are displayed.