New Approach to Generalized Two-Dimensional Correlation Spectroscopy. II: Eigenvalue Manipulation Transformation (EMT) for Noise Suppression

Abstract

This paper introduces the concept of eigenvalue manipulating transformation (EMT) of a data matrix for noise suppression in two-dimensional (2D) correlation spectroscopy. The FT-IR spectra of a polystyrene/methyl ethyl ketone/toluene solution mixture during the solvent evaporation process, to which were added a substantial amount of artificial noise, have been analyzed. By uniformly raising the power of a set of eigenvalues, the major eigenvalues become more prominent. As a consequence, minor eigenvectors representing the noise component are no longer strongly represented in the reconstructed data. This EMT operation is similar to the simple truncation of noise-dominated minor factors practiced in standard principal component analysis (PCA), as demonstrated in our preceding paper on PCA-2D correlation spectroscopy. The effect of this new EMT scheme is more gradual, with attractive flexibility to continuously fine-tune the balance between the desired noise reduction effect and the retention of pertinent spectral information.