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Data provided by most optic earth observation satellites such as IKONOS, Quick Bird and GeoEye are composed of a panchromatic channel of high spatial resolution (HR) and several multispectral channels at a lower spatial resolution (LR). The fusion of a HR panchromatic and the corresponding LR spectral channels is called "pan-sharpening". It aims at obtaining a high resolution multispectral image. In this paper, we propose a new sophisticated pan-sharpening method named Sparse Fusion of Images (SparseFI, pronounced as sparsify). SparseFI is based on the compressive sensing theory and explore the sparse representation of HR/LR multispectral image patches in the dictionaries pairs co-trained from the panchromatic image and its corresponding down-sampled version. Compared to other methods it "learns" from, i.e. adapts itself to, the data and has better performance than existing methods. Due to the fact that the SparseFI algorithm does not assume any model of the panchromatic image and thanks to the super-resolution capability and robustness of compressive sensing, it gives higher spatial and spectral resolution with less spectral distortion compared to the conventional methods.