Restricted Least Squares Estimation of the Spectra and Concentration of Two Unknown Constituents Available in Mixtures

Investigation and visualization of resolution theorems in self modeling curve resolution (SMCR) methods

“…All these feasible solutions are equally valid from a mathematical point of view and fit equally well the data matrix, although only one of them is the “true” one. This intrinsic indeterminacy of multivariate curve resolution methods is known as rotational ambiguity . However, when constraints are applied and the data structure is used appropriately, the set of feasible solutions can be limited considerably, and in favorable cases, even give a unique solution coincident with the true one.…”

Multivariate Calibration

“…This can be done, e.g., by rotation of the loading and score spaces from PCA of the mixture spectra, to attain nonnegativity in both constituent spectra and concentrations [22,28,42].…”

Multivariate Calibration Using Covariance Adjustment

“…Recently MARTENS (1982) and BROWN (1983) proposed multivariate calibration methods of this type. Brown used a generalized least squares approach and he made no assumption on the error covariance matrix of the measurement instrument.…”

“…We will consider only socalled classical calibration methods which are most commonly used in socalled controlled calibration experiments (BROWN, 1982). MARTENS (1982) and BROWN (1983) proposed multivariate calibration methods of this type. Brown used a generalized least squares approach and he made no assumption on the error covariance matrix of the measurement instrument.…”