We present an approach to learn predictive models and perform variable selection by incorporating structural information from Mass Spectral Imaging (MSI) data. We explore the use of a smooth quadratic penalty to model the natural ordering of the physical variables, that is the mass-to-charge (
) ratios. Thereby, estimated model parameters for nearby variables are enforced to smoothly vary. Similarly, to overcome the lack of labeled data we model the spatial proximity among spectra by means of a connectivity graph over the set of predicted labels. We explore the usefulness of this approach in a mouse brain MSI data set.