We present progress toward the quantitative extraction of chemical concentration profiles, component spectra, sample topography, and other information from imaging mass spectrometry data. Our approach is based on maximum a posteriori image reconstruction as used in astronomy, computer vision, hyperspectral imaging, and other fields. We propose a simple but extensible nonlinear model for the sample, consisting of concentration profiles for each component, topography, component mass spectra, and “interaction spectra” that describe the interactions between components. This model is fit against sample data using stochastic optimization techniques. This approach can naturally incorporate regularization, chemical structure identification, and matching against standard reference data. In this article, we present preliminary analyses of time-of-flight secondary ion mass spectrometry (TOF SIMS) images of a well-characterized reference sample and discuss further extensions of this approach. Copyright © 2012 John Wiley & Sons, Ltd.