The fusion of images captured from multi-modality sensors has been studied for many years. It is aiming at combining multiple sources together to maximize the meaningful information and reduce the redundancy. Meanwhile, sparse representation of images has been attracting more and more attentions. It has been effectively utilized on image reconstruction, image de-noising, super-resolution and others. In this paper, we propose an optimum function based on sparse representation model to accomplish image fusion tasks. For any pair of input source images, we first obtain their sparse vectors respectively on a pre-trained dictionary. Then we pursuit the sparse vector for the fused image by optimizing the Euclidean distances between fused image and each input, weighted by their own gradients. Optimization penalties are discussed to induce numerical or analytical solutions. And the experimental results have shown that the proposed method can effectively combine meaningful information and outperform traditional wavelet methods.