Accelerated Hyperspectral Unmixing with Endmember Variability via the Sum-Product Algorithm

The rich spectral information captured by hyperspectral sensors has given rise to a number of remote sensing applications, ranging from vegetative assessment and crop health monitoring, to military surveillance and combatant identification. However, due to limited spatial resolution, multiple ground materials generally contribute, i.e. mix, to form the spectrum recorded for a single pixel. The unmixing problem considers the inverse problem of determining the underlying material spectra, called endmembers, from sensor measurements. While classical unmixing approaches were deterministic in nature and did not attempt to identify in-scene materials, recent methods use labeled training data to generate statistical models of endmember variabilities and perform statistical unmixing for simultaneous material identification and abundance estimation.

However, the computational complexity of statistical unmixing with endmember variability is Ο(N³), cubic in the number N of sensed spectral bands. This large computational demand is at odds with continuous technological improvements that are dramatically increasing the spectral resolution of remote spectroscopy methods. In particular, current sensor technology is transitioning from the hyperspectral realm (hundreds of spectral bands) to the ultraspectral realm (thousands of spectral bands) and eclipsing the ability to perform statistical unmixing.

In this thesis we develop a computationally tractable statistical unmixing method. The proposed method uses Markov chains to model endmember variability and the spectral correlation properties present within endmembers. We use a probabilistic graphical model over multiple Markov chains to capture the mixing effects of the spectral sensor and employ sum-product message passing to develop an accelerated statistical unmixing algorithm. The computational complexity, Ο(NM³), of the proposed algorithm is only linear in the number of bands and depends on the number of endmembers M in a cubic fashion. As M is generally small and fixed (in the 10s), the accelerated algorithm represents a dramatic speed-up over existing methods. Examples demonstrate comparable error rates with two orders of magnitude reduction in computation time compared to existing statistical unmixing methods.