Ordinary and Bundle-Unmixing Approaches Under the Influence of the BRDF Effect

Remotely sensed spectral data play a vital role in interpreting and understanding land cover properties. However, due to its typically low spatial resolution, the ability to extract information from the data using traditional applications is limited to the pixel size, which, in many cases, is bigger than the phenomena of interest. On the other hand, spectral unmixing allows for extracting information from such data at the subpixel level by estimating the fractional abundance of the different land cover types within the pixel, so-called endmembers (EMs). Many approaches have been developed for this purpose. Nonetheless, the ordinary methods use only a single spectral signature for each EM, disregarding the highly probable spectral variability within each EM spectra. Therefore, bundle-unmixing methods were developed to overcome this limitation by using a set of spectra for each EM.Previous research results show the advantage of bundle-unmixing methods in enhancing the fraction estimation for various cases with an EM variability due to multiple effects. Still, despite the encouraging results, only very few works considered the spectral variability caused by the impact of the Bidirectional Reflectance Distribution function (BRDF). Thus, this work focused on studying the performance of ordinary and bundle-unmixing methods under the influence of the BRDF effect. We comparatively examined five methods, each with particular characteristics: two bundle methods and three ordinary ones; among them, one method relies on the Spectral Angle Mapper (SAM) as an objective function. We used three data sets for experimenting: 1) a laboratory set involving three land covers measured from various viewing zenith angles, 2) a synthetic data set created by simulating spectral data influenced by the BRDF effect using semi-empirical models, and 3) an areal data set including hyperspectral images over the Icelandic volcanic area. We examined the methods' performance under various signal-to-noise (SNR) ratio levels.The results clearly show the superiority of the bundle methods in reducing the effect of the BRDF on the estimated fractions. Besides, the most exciting outcome shows that despite relying on only one spectral signature per EM, the SAM-based method outperforms the other ordinary methods and provides accurate results comparable to the bundle ones. Our study aimed to understand better the complex relationship between BRDF, spectral variability, and unmixing accuracy. This investigation may enhance remote sensing data analysis and refine the unmixing approach in the presence of BRDF-induced spectral variability to improve land cover mapping and environmental monitoring using spectral data.