Resolution of severely overlapped spectra from matrix-formatted spectral data using constrained nonlinear optimization

A three-step scheme for resolving severely overlapped component spectra from bilinear 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 corresponding to this nonnegative, minimally correlated basis will be diagonal if the basis vectors happen to be feasible estimates of the component 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

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