This paper presents an algorithm based on sparse representation for fusing hyperspectral and multispectral images. The observed images are assumed to be obtained by spectral or spatial degradations of the high resolution hyperspectral image to be recovered. Based on this forward model, the fusion process is formulated as an inverse problem whose solution is determined by optimizing an appropriate criterion. To incorporate additional spatial information within the objective criterion, a regularization term is carefully designed,relying on a sparse decomposition of the scene on a set of dictionaryies. The dictionaries and the corresponding supports of active coding coefficients are learned from the observed images. Then, conditionally on these dictionaries and supports, the fusion problem is solved by iteratively optimizing with respect to the target image (using the alternating direction method of multipliers) and the coding coefcients. Simulation results demonstrate the efficiency of the proposed fusion method when compared with the state-of-the-art.