UC Santa Cruz

Hyperspectral imaging is a remote sensing technique widely used in a variety of military and environmental applications. For example, hyperspectral images can be used to detect chemical plumes invisible to the human eye, and to identify their chemical structure. A hyperspectral image is a massive cube of data consisting of thousands of pixels each with dozens of observations over a range of frequencies in the electromagnetic spectrum. Algorithms that use hypothesis testing and assume independence over pixels have shown success in detecting gas clouds, but often fail in identifying chemical components. We approach identification problems in hyperspectral imaging as a variable selection problem, which can be solved robustly by taking advantage of spatial information in the image. For this purpose we develop Bayesian spatial model selection algorithms which use mixtures of g-priors, Gaussian Markov Random Fields, and Gaussian Process Priors to account for correlation among chemicals, to induce spatial dependence among pixels, and to account for nonlinearities in pixel signals. To illustrate the performance of the models we apply them to several partially synthesized hyperspectral images and show that our method outperforms state-of-the-art algorithms, such as the LASSO and Fused LASSO.