Supervised Raman spectra estimation based on nonnegative rank deficient least squares

Raman spectroscopy is a powerful and effective technique for analyzing and identifying the chemical composition of a substance. In this paper, we focus on supervised methods for estimating Raman spectra and present a supervised method that can handle rank deficiency for estimating the Raman spectra. Earlier work has mostly assumed that the reference spectra matrix whose columns consist of the library of reference spectra are of full rank. However in practice, methods that can handle rank deficient cases, and the special case of an over complete library, are needed. We present our theoretical discovery that the active set method with a proper starting vector can actually solve the rank deficient nonnegativity-constrained least squares problems without ever running into rank deficient least squares problems during iterations. Experimental results illustrate the effectiveness of the proposed approaches.