Probabilistic Mixture Modeling For End-Member Extraction in Hyperspectral Data

Imaging spectrometers produce data with both spatial and spectroscopic resolution, a technique known as hyperspectral imaging (HSI). In a typical setting, the purpose of HSI is to disentangle a microscopic mixture of several material components in which each contributes a characteristic spectrum--often confounded by self-absorption effects, observation noise and other distortions. We outline a Bayesian mixture model enabling probabilistic inference of end member fractions while explicitly modeling observation noise and resulting inference uncertainties. We generate synthetic datasets and use Hamiltonian Monte Carlo to produce posterior samples that yield, for each set of observed spectra, an approximate distribution over end member coordinates. We find the model robust to the absence of pure (i.e. unmixed) observations as well as to the presence of non-isotropic Gaussian noise, both of which cause biases in the reconstructions produced by N-FINDER and other widespread end-member extraction algorithms.