Reconstruction for MR spectroscopic imaging (MRSI) is a challenging problem where incorporation of spatiospectral prior information is often necessary. While spectral constraints have been effectively utilized in the form of temporal basis functions, spatial constraints are often imposed using spatial regularization. In this work, we present a new kernel-based method to incorporate a priori spatial information, which was motivated by the success of kernel-based methods in machine learning. It provides a new mechanism for constrained image reconstruction, effectively incorporating a priori spatial information. The proposed method has been evaluated using both simulation and in vivo data, producing very impressive results. This new reconstruction scheme can be used to process any MRSI data, especially those from high-resolution MRSI experiments.