Two-dimensional correlation and codistribution spectroscopy (2D-COS and 2D-CDS) analyses of planar spectral image data

Abstract

Application of 2D correlation and codistribution analyses to spectral image data is explored. While traditional 2D correlation or codistribution analysis based on one perturbation variable may be applied for a simple line scan sampling of the image data along a single curve, 2D correlation analysis for a planar image data with two independent spatial coordinates becomes more complicated. Synchronous spectrum not affected by the sampling order may be obtained for planar spectral image data, but asynchronous spectrum involving the Hilbert transformation along a perturbation direction cannot be unambiguously defined for planar data. Instead, disrelation spectrum derived from synchronous spectrum may be used to identify characteristic bands of different species contributing to the spectral image. While horizontal or vertical unfolding of image data can convert the planar data into a concatenated dataset with a linear structure for asynchronous analysis, some ambiguity remains about the mixed directional information caused by the concatenation order dependence of the Hilbert transformation. Vertical or horizontal bundling or averaging operations remove such ambiguity to generate directionally sensitive asynchronous correlation or codistribution spectra.