Constrained image reconstruction incorporating prior information has been widely used to overcome the ill-posedness of reconstruction problems. In this work, we propose a novel "kernel+sparse" model for constrained image reconstruction. This model represents the desired image as a function of features "learned" from prior images plus a sparse component that captures localized novel features. The proposed method has been validated using multiple MR applications as example. It may prove useful for solving a range of image reconstruction problems in various MR applications where both prior information and localized novel features exist.