Raman spectroscopy has received a great deal of attention in recent years in the chemical and biological detection
research community because of its unique ability to determine the chemical composition of substances. This has led to
development of fast and numerically efficient algorithms for Raman spectra estimation. There are two types of
algorithms for Raman spectra estimation, namely supervised and unsupervised. In the supervised approach, a number of
reference spectra for known chemicals is used. It is also assumed that the measured spectra of one or more unknown
substances belong to one of the individual substances in the reference library, or that they originate from a linear
combination of a number of reference spectra. The mixing coefficients for a measured spectrum are often estimated
using the nonnegative least squares (NNLS) or nonnegative weighted least squares (NNWLS) algorithms. This is a
constrained parameter estimation problem due to the inherent nonnegativity of the mixing coefficients.
Some previous researchers have used the NNLS method, in which no weight matrix is used, or all measurement error
variances are treated as equal. In our Fusion 2009 paper, we found that the measurement error variances or weights
vary significantly with the wavenumber and that it is therefore necessary to use non-uniform weights in parameter
estimation. Previously we used the true weights and have done limited study using estimated weights. In this paper, we
perform extensive study for Raman spectra estimation using WLS and NNWLS for one, two, and three chemicals, using
simulated data and Monte Carlo simulations.