Journal article
An improved spectral reconstruction method based on non-negative matrix factorization and multiplicative update rule: Framework and preliminary application on TROPOMI BRDF in 400-2400 nm
Journal of quantitative spectroscopy & radiative transfer, Vol.365, 110140
09/21/2026
DOI: 10.1016/j.jqsrt.2026.110140
Abstract
•A physically interpretable NMF framework reconstructs continuous 400–2400 nm spectra from TROPOMI BRDF.•A fully vectorized multiplicative update algorithm enables efficient non-negative coefficient optimization.•The proposed MU framework improves reconstruction over conventional least-squares fitting.•MODIS NBAR and EMIT validations demonstrate robust spatial and hyperspectral reconstruction performance.
This study presents a physically interpretable hyperspectral reconstruction framework based on Non-negative Matrix Factorization (NMF) with multiplicative update (MU) optimization to reconstruct continuous hyperspectral surface reflectance from satellite bidirectional reflectance distribution function (BRDF) products with limited spectral bands. The Sentinel-5P/TROPOMI BRDF monthly product generated using the Generalized Retrieval of Atmosphere and Surface Properties (GRASP) algorithm is extended from seven discrete spectral bands to a continuous spectral range of 400–2400 nm. Five representative spectral basis vectors extracted from the USGS/ASTER spectral libraries are combined with MU-based mixing-coefficient optimization to ensure physically meaningful, non-negative reconstruction. Compared with the conventional least-squares solution, the proposed MU optimization yields more robust non-negative coefficient estimation and consistently improves hyperspectral reconstruction performance. The reconstructed hyperspectral BRDF parameters exhibit physically consistent spatial distributions and pronounced seasonal variations across North America. Validation against monthly mean MODIS MCD43C4 Nadir BRDF-Adjusted Reflectance (NBAR) demonstrates excellent agreement in the visible and near-infrared regions (470–859 nm), with monthly mean differences generally within ±0.01 and standard deviations of 0.02–0.04. In the shortwave infrared, larger discrepancies are observed over vegetation-dominated regions, where the monthly mean differences range from approximately −0.06 to −0.04 at 1240 and 1610 nm. Independent comparisons with EMIT Level-2A hyperspectral surface reflectance further confirm that the reconstructed spectra successfully reproduce the dominant hyperspectral characteristics of representative natural surfaces across the continuous 400–2400 nm spectral range. Despite the remaining shortwave-infrared underestimation, likely reflecting the limited representation of vegetation spectral variability in the selected spectral dataset, both the MODIS and EMIT validations confirm the overall robustness of the proposed framework. The proposed MU-based NMF framework provides a transparent solution for reconstructing continuous hyperspectral reflectance from satellite products with limited spectral bands, establishing a scalable methodological foundation for future cross-sensor harmonization and multi-resolution surface reflectance reconstruction.
Details
- Title: Subtitle
- An improved spectral reconstruction method based on non-negative matrix factorization and multiplicative update rule: Framework and preliminary application on TROPOMI BRDF in 400-2400 nm
- Creators
- Weizhen Hou - Smithsonian InstitutionJun Wang - University of IowaXiong Liu - Center for Astrophysics Harvard & SmithsonianCheng Chen - Laboratoire d'Optique AtmosphériqueXiaoguang Xu - University of Maryland, Baltimore County
- Resource Type
- Journal article
- Publication Details
- Journal of quantitative spectroscopy & radiative transfer, Vol.365, 110140
- DOI
- 10.1016/j.jqsrt.2026.110140
- ISSN
- 0022-4073
- eISSN
- 1879-1352
- Publisher
- Elsevier Ltd; OXFORD
- Grant note
- NASA TEMPO grant: NNL13AA09C Smithsonian Astrophysical Observatory's subaward: S03939-01, 80NSSC22K1047
This research was supported by the NASA TEMPO grant (NNL13AA09C) and Smithsonian Astrophysical Observatory's subaward S03939-01 to NASA grant (80NSSC22K1047). Besides, J. Wang's contribution is made possible by in-kind support through the Lichtenberger Family Chair Professor in Chemical Engineering at the University of Iowa. The authors express their sincere gratitude to Haesun Park from the School of Computational Science and Engineering at the Georgia Institute of Technology for providing the NMF_BPAS toolbox, which implements alternating non-negativity-constrained least squares and block principal pivoting/active set methods (https://faculty.cc.gatech. edu/~hpark/nmfbpas.html). We also acknowledge the use of the M_Map mapping package for MATLAB (University of British Columbia) in generating the geographic visualizations and cartographic projections presented in this study (https://www-old.eoas.ubc.ca/~rich/map. html). Meanwhile, we acknowledge the use of the MODIS MCD43C4 Collection 6.1 Nadir BRDF-Adjusted Reflectance (NBAR) product provided by the NASA Land Processes Distributed Active Archive Center (LP DAAC). We also gratefully acknowledge the U.S. Geological Survey (USGS) Spectral Library for providing valuable hyperspectral surface reflectance measurements used in this study. Furthermore, we acknowledge the use of the ASTER Spectral Library, which is now distributed as part of the ECOSTRESS Spectral Library maintained by the Jet Propulsion Laboratory (JPL) and NASA. Finally, we gratefully acknowledge NASA Earthdata for providing access to the EMIT Level-2A Estimated Surface Reflectance and Uncertainty and Masks (EMI-TL2ARFL, Version 001) dataset through the Earthdata Search portal.
- Language
- English
- Electronic publication date
- 09/21/2026
- Academic Unit
- Electrical and Computer Engineering; Civil and Environmental Engineering; Physics and Astronomy; Chemical and Biochemical Engineering
- Record Identifier
- 9985237504502771
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