Projection two-dimensional correlation analysis

Projection 2D correlation analysis, which may potentially become a useful tool in the simplification of highly congested 2D correlation spectra often encountered in practice, is introduced. By taking advantage of the fact that 2D correlation spectra can be expressed in terms of matrix multiplications of spectral data, one can apply matrix-based projection and null-space projection operations as an effective filtering tool to transform spectral data to generate new 2D correlation spectra with much more simplified features. Projection matrices used in this approach can be generated from various sources, including a part of original spectral data, other spectra of different origin, perturbation variables, or even arbitrarily chosen mathematical functions. Furthermore, by linearly combining the projected and null-space projected spectra, application of a series of oblique projections to gradually attenuate or augment select features is also possible. Projection 2D correlation analysis applied to the ATR IR study of time-dependent compositional changes of a solution mixture demonstrated its ability to obtain pure component 2D spectra, 2D spectra based on contributions of a reduced number of species, and various 2D spectra with specific features selectively accentuated, to assist the unambiguous interpretation of complex and highly overlapped spectral data.