SEPARATION OF ADDITIVE MIXTURE SPECTRA BY A SELF-MODELING METHOD

A method for the separation of additive spectra of complex mixtures is developed on the basis of a linear algebra technique and nonlinear op timization algorithms. It is shown to be possible, under certain condi tions, to uniquely separate a set of complex spectral curves consistin g of the same components, but with different proportions, into the unk nown spectra of the pure constituents and to give their respective rel ative concentrations. The method proposed is a variant of the self-mod eling curve-resolution approach based on the singular value decomposit ion of the data matrix formed by the set of digitized spectra of mixtu res. The spectra of components are calculated as linear combinations o f left-side singular vectors of the data matrix provided that both ind ividual spectra and their concentrations are nonnegative and the shape s of the spectra are as dissimilar as possible. The technique provides a unique decomposition if each fundamental spectrum has at least one wavelength with zero intensity and the other pure spectra are nonzero at this wavelength. The algorithm is evaluated on an artificial data s et to clearly demonstrate the method. The approach described in this p aper may be applied to any experiment whose outcome is a continuous cu rve y(x) that is a sum of unknown, nonnegative, linearly independent f unctions.