A physics-based unmixing method to estimate subpixel temperatures on mixed pixels

This paper presents a new algorithm for the analysis of linear spectral mixtures in the thermal infrared domain, with the goal to jointly estimate the abundance and the subpixel temperature in a mixed pixel, i.e., to estimate the relative proportion and the temperature of each material composing the mixed pixel. This novel approach is a two-step procedure. First, it estimates the emissivity and the temperature over pure pixels using the standard temperature and emissivity separation (TES) algorithm. Second, it estimates the abundance and the subpixel temperature using a new unmixing physics-based model, called Thermal Remote sensing Unmixing for Subpixel Temperature (TRUST). This model is based on an estimator of the subpixel temperature obtained by linearizing the black body law around the mean temperature of each material. The abundance is then retrieved by minimizing the reconstruction error with the estimation of the subpixel temperatures. The TRUST method is benchmarked on simulated scenes against the fully constrained least squares unmixing applied on the radiance and on the estimation of surface emissivity using the TES algorithm. The TRUST method shows better results on pure and mixed pixels composed of two materials. TRUST also shows promising results when applied on thermal hyperspectral data acquired with the Thermal Airborne Spectrographic Imager during the Detection in Urban scenario using Combined Airborne imaging Sensors campaign and estimates coherent localization of mixed-pixel areas.