Resolution of Severely Overlapped Spectra from Matrix-Formated Spectral Data Using Constrained Nonlinear Optimization

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A three-step scheme for resolving severely overlapped component spectra from billnear matrix-formated data Is reported. After the number of sample components Is determined, a positive basis Is first formed consisting of the most dissimilar rows and columns of the matrix. The concentration factor matrix (CFM) corresponding to this nonnegative, minimally correlated basis will be diagonal If the basis vectors happen to be feasible estimates of the component spectra. When the CFM Is not diagonal, a constrained nonlinear optimization routine Is used In a second step to reduce the off-diagonal elements of the CFM to zero while maintaining the nonnegativity of the estimated spectra. In many cases, the nonnegativity and feasibility constrains are not sufficient to produce a unique set of component spectra estimates. Other criteria, such as the degree of overlap of the resolved spectra, may be used as the basis of a third step to generate an arbitrary, but unique, choice among the feasible estimates of the component spectra. The performance of this scheme is evaluated by analyzing synthetic and experimental fluorescence excitation-emission matrices (EEMs) exhibiting various levels of spectra overlap and random noise. Coincident spectra can be resolved from an EEM by using this approach In the case of some EEMs of rank greater than two. Evaluations using synthetic data Indicate that this scheme can be applied to EEMs that have signal-to-nolse ratios above 18. Successful resolution of experimental three- and four-component mixtures is Illustrated. © 1990, American Chemical Society. All rights reserved.

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Analytical Chemistry

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