Noise perturbation in functional principal component analysis filtering for two-dimensional correlation spectroscopy: its theory and application to infrared spectra of a poly(3-hydroxybutyrate) thin film.

A method based on noise perturbation in functional principal component analysis (NPFPCA) is for the first time introduced to overcome the noise interference problem in two-dimensional correlation spectroscopy (2D-COS). By the systematic addition of synthetic noise to the dynamic multivariate spectral data, the functional principal component analysis (FPCA) described in this report is able to accurately determine which eigenvectors are representing significant signals instead of noise in the original data. This feature is especially useful for the data reconstruction and noise filtering. Reconstructed data resulted from the smooth eigenvectors can produce much more reliable 2D correlation spectra by removing the correlation artifacts from noise, which in turn enable more accurate interpretation of the spectral variations. The usefulness of this method is demonstrated with a theoretical framework and applications to the 2D correlation analyses of both simulated data and temperature-dependent reflection-absorption infrared spectra of a poly(3-hydroxybutyrate) (PHB) thin film.