A Reproducible Framework for Blind Evaluation of Hyperspectral Endmember Extraction Algorithms Under Spectral Variability and Band Selection

Hyperspectral unmixing aims to decompose mixed pixels into a collection of pure material signatures, known as endmembers, and estimate their corresponding fractional abundances. However, high intrinsic dimensionality and spectral redundancy often degrade the accuracy of Endmember Extraction (EE) algorithms. This paper presents a comprehensive comparative analysis of six geometric EE algorithms to evaluate their robustness, computational efficiency, and spatial stability. The evaluated methods include Vertex Component Analysis (VCA), N-FINDR, Pixel Purity Index (PPI), Automatic Target Generation Process (ATGP), Sequential Growth Algorithm (SGA), and the Convex-Cone model (SVMAX). The experiments are conducted on the DLR Hyperspectral Unmixing (DLR HySU) benchmark dataset. This dataset is a publicly available resource developed by the German Aerospace Center to address the critical shortage of real-world hyperspectral data with reliable sub-pixel ground truth for validating unmixing algorithms. Acquired over the DLR premises in Oberpfaffenhofen using an airborne HySpex VNIR spectrometer alongside simultaneous high-resolution RGB imagery and ground-based field spectrometer measurements, the dataset features a controlled scenario of five distinct synthetic materials—bitumen, red metal, and red, blue, and green fabric—placed as square targets in five varying sizes (from 0.25 m to 3 m) atop a homogeneous grass background. This dataset also comprises 135 spectral bands, covering a wavelength range from approximately 417 nm to 903 nm. To mitigate noise and redundancy, an Orthogonal Projection-Based Band Selection (OPBS) technique is implemented, compressing the data from 135 to 45 highly informative bands. Subsequently, the Fully Constrained Least Squares (FCLS) method is employed for abundance estimation. The performance is quantitatively evaluated using the Spectral Angle Mapper (SAM), Root Mean Square Error (RMSE), and spatial invariance, further validated by ideal reference maps and pixel-wise image reconstruction analysis. Results demonstrate that deterministic approaches (SVMAX, SGA) and stabilized random-projection methods (VCA) exhibit robust performance under the OPBS configuration, achieving SAM errors below 3.5° and RMSEs under 0.009, while maintaining high physical fidelity to the Linear Mixture Model (LMM). Notably, OPBS significantly accelerated computational feasibility, enabling SVMAX to complete extraction in just 0.0036 seconds and boosting VCA's speed by a factor of 3.6. The study proves that targeted band selection rigorously stress-tests extraction algorithms, acting as a critical structural stabilizer that improves unmixing accuracy and computational efficiency.