Matrix-R Theory: A Simple Generic Method to Improve RGB-Guided Spectral Recovery Algorithms ^†

RGB-guided spectral recovery algorithms include both spectral reconstruction (SR) methods that map image RGBs to spectra and pan-sharpening (PS) methods, where an RGB image is used to guide the upsampling of a low-resolution spectral image. In this paper, we exploit Matrix-R theory in developing a post-processing algorithm that, when applied to the outputs of any and all spectral recovery algorithms, almost always improves their spectral recovery accuracy (and never makes it worse). In Matrix-R theory, any spectrum can be decomposed into a component—called the fundamental metamer—in the space spanned by the spectral sensitivities and a second component—the metameric black—that is orthogonal to this subspace. In our post-processing algorithm, we substitute the correct fundamental metamer, which we calculate directly from the RGB image, for the estimated (and generally incorrect) fundamental metamer that is returned by a spectral recovery algorithm. Significantly, we prove that substituting the correct fundamental metamer always reduces the recovery error. Further, if the spectra in a target application are known to be well described by a linear model of low dimension, then our Matrix-R post-processing algorithm can also exploit this additional physical constraint. In experiments, we demonstrate that our Matrix-R post-processing improves the performance of a variety of spectral reconstruction and pan-sharpening algorithms.