Abstract : In this work we propose a method for the fusion of hyperspectral (HS) and multispectral (MS) satellite images. The aim of the fusion process is to merge the spectral quality of the HS images with the better spatial resolution of the MS images. The final result is an image having both high spectral and spatial resolution. In order to perform the fusion task, we suggest an approach based on optimal transport theory that highlights the idea of energy transfer from the starting images HS and MS to the resulting final image. In this sense, the map transport can be thought as the transfer of characteristics of one image to another.