Bayesian Temperature Emissivity Separation Using Copula Chain Models

Hyperspectral sensing in the long-wave infrared (LWIR) domain is complicated by the ambiguity between a material’s temperature and its emissivity—a problem known as temperature-emissivity separation (TES). In this letter, we develop a Bayesian approach to the TES problem that disambiguates emissivity values through a novel prior that uses a copula-based Markov chain model. While supporting efficient posterior inference through the forward-backward algorithm, the proposed copula chain improves emissivity retrieval performance by enforcing physical $[{0, 1}]$ emissivity bounds and capturing interband correlation. Numerical results demonstrate significant improvement over the existing methods, including a 54% reduction in emissivity estimation error relative to the least-squares TES (LS-TES) algorithm for a 20 microflick noise level. Finally, the posterior uncertainty characterization of the proposed Bayesian algorithm is expected to aid subsequent exploitation tasks, such as material classification and sensor fusion.