In this paper we present a comparison of different schemes for transform coding of reflectance spectra. Aiming for representing the spectra with a small number of coefficients, we first concentrate on schemes using orthonormal sets of basis vectors. In this case the basis vector sets used for analysis and synthesis of the spectra are identical. Regarding the mean squared spectral error, the optimal basis function set for a given set of test spectra can be calculated analytically.We then allow the vector bases for analysis and synthesis to be different and give an example for creating appropriate sets. We show that the best vector set strongly depends on the error measure that is to be minimized. It is not efficient to replace the error in a visually uniform color space by the mean squared spectral error. Minimizing these two error measures yields different sets of vectors as they can not be minimized simultaneously. Furthermore we show the superiority of the approach using separate analysis and synthesis vector sets over orthonormal basis vector sets.In order to verify the results of the analytically derived vector sets, we compare them with those of vector sets derived by optimization algorithms.
Werner Praefcke, "Analysis-synthesis transforms versus orthogonal transforms for coding reflectance spectra" in Proc. IS&T 5th Color and Imaging Conf., 1997, pp 177 - 181, https://doi.org/10.2352/CIC.1997.5.1.art00035