Compressed Raman classification method with upper-bounded error probability

Classification of different species with Raman measurements is analyzed when a total of exactly $ N $N photons are detected with binary filtered Raman spectra instead of fixing the measuring time. The optimal classification method for this problem leads to classification error probabilities upper-bounded by the Bhattacharyya bound and that are invariant to the multiplication of the spectrum intensities by an unknown factor. Furthermore, it is shown that this approach can be implemented with a number of binary filters smaller than the number of species to discriminate.