Unmixing urban hyperspectral imagery with a Gaussian mixture model on endmember variability

Spectral unmixing given a library of endmember spectra can be achieved by multiple endmember spectral mixture analysis (MESMA), which tries to find the optimal combination of endmember spectra for each pixel by iteratively examining each endmember combination. However, as library size grows, computational complexity increases which often necessitates a laborious and heuristic library reduction method. In this paper, we model a pixel as a linear combination of endmembers sampled from probability distributions of Gaussian mixture models (GMM). The parameters of the GMM distributions are estimated using spectral libraries. Abundances are estimated based on the distribution parameters. The advantage of this algorithm is that the model size grows very slowly as a function of the library size. To validate this method, we used data collected by the AVIRIS sensor over the Santa Barbara region: two 16 m spatial resolution and two 4 m spatial resolution images. 64 validated regions of interest (ROI) (180 m by 180 m) were used to assess estimate accuracy. Ground truth was obtained using 1 m images leading to the following 6 classes: turfgrass, non-photosynthetic vegetation (NPV), paved, roof, soil, and tree. Spectral libraries were built by manually identifying and extracting pure spectra from both resolution images, resulting in 3,287 spectra at 16 m and 15,426 spectra at 4 m. We then unmixed ROIs of each resolution using the following unmixing algorithms: the setbased algorithms MESMA and AAM, and the distribution-based algorithms GMM, NCM, and BCM. The original libraries were used for the distribution-based algorithms whereas set-based methods required a sophisticated reduction method, resulting in reduced libraries of 61 spectra at 16 m and 95 spectra at 4 m. The results show that GMM performs best among the distributionbased methods, producing comparable accuracy to MESMA, and may be more robust across datasets.