Subspace-Based Temperature and Emissivity Separation Algorithms in LWIR Hyperspectral Data

In this paper, we investigate the temperature and emissivity separation (TES) problem from hyperspectral data acquired in the long-wave infrared region (LWIR) of the electromagnetic spectrum. We derive a general class of TES algorithms [subspace-based TES (SBTES)] relying on the assumption that the emissivity spectra of natural and man-made materials can be well represented in a given subspace of the original data space. Specifically, by exploiting the subspace representation and the Gaussian model for the noise affecting LWIR hyperspectral data, we approach TES under a statistical perspective by obtaining the maximum likelihood estimates of both the temperature and the spectral emissivity. The proposed approach originates several algorithms whose specific form depends on the particular basis matrix adopted to address the emissivity subspace. We study the performance of the presented class of algorithms and derive theoretical bounds on the accuracy of the temperature and emissivity estimators. Furthermore, by specifying two basis matrices for the emissivity subspace, we propose two different algorithms within the SBTES class. Finally, we present the results of an extensive experimental analysis carried out over simulated data to assess and compare the performance of the two presented algorithms.