To drive the application of surface-enhanced Raman spectroscopy (SERS) mapping in ex vivo diagnostic imaging and non-biological material characterization, we have designed a robust and accurate multiplex spectral fitting method using an alternating minimization algorithm to extract individual constituent Raman spectra with very small overall fitting error (as low as 2%). For each mixed Raman signal, constituent spectra and mixture coefficients were estimated jointly based on reference spectra that were measured in the lab. Our method is based on a Poisson model to reflect the photon counting nature of Raman signals and includes the nonlinear noise in the measured data, making our method robust against data containing relatively large random noise. In our method, we minimized a cost function consisting of two terms: (1) the overall fitting error between the measured and modeled spectra and (2) the sum of the individual error between each reference spectrum and its corresponding constituent. This method inherently guarantees that the estimates will approach the global minimum with monotonic convergence. The accuracy of our method was validated by applying it to a SERS spectral fitting problem and comparing our results to those from existing methods. Copyright © 2013 John Wiley & Sons, Ltd.