Preprocessing Algorithm Leveraging Geometric Modeling for Scale Correction in Hyperspectral Images for Improved Unmixing Performance

Spectral variability significantly impacts the accuracy and convergence of hyperspectral unmixing algorithms. Many methods address complex spectral variability; yet large-scale distortions to the scale of the observed pixel signatures due to topography, illumination, and shadowing remain a major challenge. These variations often degrade unmixing performance and complicate model fitting. Because of this, correcting these variations can offer significant advantages in real-world GIS applications. In this paper, we propose a novel preprocessing algorithm that corrects scale-induced spectral variability prior to unmixing. By estimating and correcting these distortions to the scale of the pixel signatures, the algorithm produces pixel signatures with minimal distortions in scale. Since these distortions in scale (which hinder the performance of many unmixing methods) are greatly minimized in the output provided by the proposed method, the abundance estimation of the unmixing algorithms is significantly improved. We present a rigorous mathematical framework to describe and correct for scale variability and provide extensive experimental validation of the proposed algorithm. Furthermore, the algorithm's impact is evaluated across a wide range of state-of-the-art unmixing methods on two synthetic and two real hyperspectral datasets. The proposed preprocessing step consistently improves the performance of these algorithms, achieving error reductions of around 50%, even for algorithms specifically designed to handle spectral variability. This demonstrates that scale correction acts as a complementary step, facilitating more accurate unmixing with existing methods. The algorithm's generality, consistent impact, and significant influence highlight its potential as a key component in practical hyperspectral unmixing pipelines. The implementation code will be made publicly available upon publication.