Unmixing Hyperspectral imagery is a complex problem. It takes into account a large number of observations, where each response is multivariate and high dimensional. At each pixel, information regarding a relatively large number of bands (e.g., L=114 bands) is recorded. The L-dimensional spectrum in a single pixel constitutes a response. The spectrum observed at each pixel is a mixture of the spectrum of different materials, known as endmembers. The goal is to determine, at each pixel, the proportion contributed by each endmember to the observed spectrum. Additionally, given that proximate pixels tend to share similar environmental conditions, accounting for spatial dependence is essential to build suitable inferential approaches to analyze these data and generate out-of-sample prediction. The number of pixels (n) may range between n~105—107, which makes this computational prohibitive. First, for each pixel, a vector of weights is estimated with as many entries as endmembers (R) are available, so that n*R regression coefficients are to be estimated. Additionally, estimating the spatial dependence modeled through a covariance function requires ~n3floating point operations. As such, model-based strategies, which provide uncertainty equipped statistical inference, are commonly avoided.
We develop a fully Bayesian strategy that massively reduces the computational burden, and allows inference and prediction with associated uncertainty estimates. First, using Dirichlet processes, we identify clusters of pixels that share a similar mix of endmember composition; such that, instead of each pixel having its own vector of coefficients, all pixels in a cluster share a single vector. Second, we obtain spatial dependence estimates using Nearest Neighbor Gaussian Processes, which reduce the number of operations to ~n. Our approach is tested on a large dataset collected over the Bonanza Creek Experimental Forest in Alaska.