Evaluation of linear models for spectral reflectance dimensionality reduction

It has been shown that dimensionality reduction techniques can be applied to a large dataset of spectral reflectance to reconstruct the spectra by the linear model with a small number of basis functions. Principal Component Analysis (PCA) and Independent Component Analysis (ICA) are two popular techniques to perform the dimensionality reduction. For each technique, there are two approaches to perform the spectral reconstruction. One approach is to use the mean-centered data while another approach excludes the mean offset. This paper presents these four linear models mathematically. The colorimetric and spectral accuracy of the spectral reconstructions using the four models were compared. It was found that ICA had slightly better performance than PCA using not only the mean-centered data but also the data excluding the mean offset. More importantly, ICA without the mean had very close performance to PCA with the mean.