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

Finlayson, Graham D., Kucuk, Abdullah and Lin, Yi-Tun (2025) Matrix-R Theory: A Simple Generic Method to Improve RGB-Guided Spectral Recovery Algorithms. Sensors, 25. ISSN 1424-8220

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Abstract

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.

Item Type:	Article
Additional Information:	Data Availability Statement Two publicly available datasets were used in this study. First, BGU ICVL Hyperspectral Dataset, which can be accessed via: https://icvl.cs.bgu.ac.il/pages/researches/hyperspectral-imaging.html (accessed: 22 July 2025). Second, the CAVE Multispectral Image Dataset, which can be accessed via: https://cave.cs.columbia.edu/repository/Multispectral (accessed: 1 December 2025).
Uncontrolled Keywords:	spectral reconstruction; spectral super-resolution; pan-sharpening; spectral image fusion; matrix-r,computer vision and pattern recognition ,/dk/atira/pure/subjectarea/asjc/1700/1707
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Colour and Imaging Lab
Depositing User:	LivePure Connector
Date Deposited:	16 Mar 2026 15:30
Last Modified:	16 Mar 2026 16:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/102353
DOI:	10.3390/s25247662

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