In quantitative susceptibility mapping (QSM), constrained dipole inversion is often necessary to overcome the ill-posedness of the underlying dipole deconvolution problem. Existing methods achieve this by the use of spatial regularization. In this work, we propose a novel "kernel+sparse" model for constrained dipole inversion. In this model, the kernel term absorbs the prior information by representing the susceptibility as a function of prior features while the sparse term accounts for the localized novel features. The proposed method has been evaluated using both simulated and in vivo data, producing impressive results. This method may prove to be useful for many QSM studies.