Abundance Estimation Methods in Spectral Unmixing for Real Data

Abstract. Spectral unmixing estimates the fractional abundances of materials, having associated spectra called endmembers, in pixels acquired by imaging spectrometers. Validation of abundance estimation methods typically relies on synthetic data or comparisons to results obtained by other algorithms. This study considers results of typical abundance estimation algorithms on the DLR HySU (Hyper-Spectral Unmixing) benchmark dataset, which contains actual imaging spectrometer data acquired over several arrangements of known-size material patches for physically traceable validation. Abundance estimates are compared against measured target areas in pixels with different degrees of mixtures. We evaluate least squares and sparse unmixing methods across different noise scenarios on real data, and by contaminating the library through addition of non-relevant endmembers. Additionally, as a way to approximate hard sparsity constraints, we enforce cardinality constraints on endmember subsets, identifying those minimizing abundance errors relative to the full library. Results suggest that fully constrained least squares yields usually the best results, but struggles in cases of highly mixed pixels. Finally, we test quantization of abundance values as a way to enforce sparsity in non-negative least squares with limited but encouraging results. Overall, the increase in accuracy of results enforcing sparse solutions supports the use of computationally efficient sparse unmixing methods in practical scenarios, part of which may become feasible if quantum computing capabilities improve in the future.