4D spatiotemporal images can be naturally divided into the background component, which is temporally coherent, and the motion component, which is spatially sparse, up to the proper basis. And this divide-and-conquer decomposition is an effective sparse representation of 4D images for the purpose of image reconstruction. Based on this prior fact, we introduce Prior Rank, Intensity and Sparsity Model (PRISM): the temporal coherence of the background component is enforced by the rank regularization and the spatial sparsity of the motion component is promoted by the sparsity regularization. In particular, the framelet based PRISM with the multi-resolution and multi-filtered structure will be utilized for image reconstruction. The superior performance of PRISM will be demonstrated with a few new medical imaging applications, including 4D cone beam CT, spiral MRI, and fused MRI-CT multi-modality.