Spectral Variability Augmented Sparse Unmixing of Hyperspectral Images

Spectral unmixing expresses the mixed pixels existing in hyperspectral images as the product of endmembers and their corresponding fractional abundances, which has been widely used in hyperspectral imagery analysis. However, the endmember spectra even for pixels from the same material of an image may include variability due to the influence of lighting conditions and inherent properties of materials within different pixels. Though the
in situ
spectral library has been used to accommodate such variability by using multiple
in situ
spectra to represent each kind of material, the performance improvement may be restricted due to the limited number of endmembers for each material. Therefore, in this article, spectral variability is directly extracted from an
in situ
endmember library and considered to be transferable among different endmembers for the first time. Furthermore, such a spectral variability is further used to augment sparse unmixing by synchronously performing endmember-based reconstruction and spectral variability-augmented reconstruction in the sparse unmixing model. By, respectively, imposing sparse and smoothness regularization over abundances and variability coefficients, a convex optimization-based spectral variability augmented sparse unmixing (SVASU) is finally proposed, and its convergence performance is also analyzed. Experiments conducted over synthetic and real-world datasets demonstrate that the proposed SVASU method not only significantly improves the unmixing performance of conventional spectral library-based unmixing but also outperforms several state-of-the-art sparse unmixing algorithms.