Different image fusion systems have been developed to deal with the massive amounts of image data for different applications, such as remote sensing, computer vision, and environment monitoring. However, the generalizability and versatility of these fusion systems remain unknown. This article proposes an efficient regularization framework to achieve different kinds of fusion tasks accounting for the spatiospectral and spatiotemporal variabilities of the fusion process. A joint minimization functional is developed by taking an advantage of a composite regularizer for enforcing joint sparsity in the gradient domain and the frame domain. The proposed composite regularizer is composed of the Hessian Schatten-norm regularization and contourlet-based regularization terms. The resulting problems are solved by the alternating direction method of multipliers (ADMM). The effectiveness of the proposed method is validated in a variety of image fusion experiments: 1) hyperspectral (HS) and panchromatic image fusion; 2) HS and multispectral image fusion; 3) multitemporal image fusion (MIF); and 4) multi-image deblurring. Results show promising performance compared with state-of-the-art fusion methods.