On including nonlinearity inmultivariate analysis of imaging SIMS data

We present progress toward the use of nonlinear models in multivariate analysis of imaging mass spectrometry data. Specifically, we consider the ion intensity at each mass and position as a nonlinear function of the concentrations of all species present. By expanding this function in a Taylor series, we both recover the precise meaning of the mass spectrum in standard bilinear analyses and introduce new 'correlation spectra' that describe matrix effects. Some fundamental results concerning the behavior of the resulting model (to second order) are presented. A numerical demonstration consisting of the analysis of synthetic data sets with known nonlinearity is also performed, which shows that the application of these ideas is computationally tractable under reasonable conditions.