Constrained Regularization:  Hybrid Method for Multivariate Calibration

We present a hybrid multivariate calibration method, constrained regularization (CR), and demonstrate its utility via numerical simulations and experimental Raman spectra. In this new method, multivariate calibration is treated as an inverse problem in which an optimal balance between model complexity and noise rejection is achieved with the inclusion of prior information in the form of a spectral constraint. A key feature is that the constraint is incorporated in a flexible manner, allowing the minimization algorithm to arrive at the optimal solution. We demonstrate that CR, when used with an appropriate constraint, is superior to methods without prior information, such as partial least-squares, and is less susceptible to spurious correlations. In addition, we show that CR is more robust than methods in which the constraint is rigidly incorporated, such as hybrid linear analysis, when the exact spectrum of the analyte of interest as it appears in the sample is not available. This situation can occur as a result of experimental or sample variations and often arises in complex or turbid samples such as biological tissues.