Comparison between statistical and optimization methods in accessing unmixing of spectrally similar materials

Abstract

This paper reports on the results from ordinary least squares and ridge regression as statistical methods, and is compared to numerical optimization methods such as the stochastic method for global optimization, simulated annealing, particle swarm optimization and limited memory Broyden-Fletcher-Goldfard-Sharon bound optimization method. We used each of the above mentioned methods in estimating the abundances of spectrally similar iron-bearing oxide/hydroxide/sulfate minerals in complex synthetic mixtures simulated from hyperspectral data. In evaluating the various methods, spectral mixtures were generated with varying linear proportions of individual spectra from the United States Geological Survey (USGS) spectral library. We conclude that ridge regression, simulated annealing and particle swarm optimization outperforms ordinary least squares method and the stochastic method for global optimization algorithms in estimating the partial abundance of each endmember. This result was independent of the error from either a uniform or gaussian distribution. For large remote sensing scenes, typically with millions of pixels and with many endmembers, we recommend using ridge regression.