Emissivity and Temperature Assessment Using a Maximum Entropy Estimator: Structure and Performance of the MaxEnTES Algorithm

In this paper, we discuss the structure and performance of the maximum entropy temperature-emissivity separation (MaxEnTES) algorithm for assessing land temperature and emissivity from thermal infrared hyperspectral images. This procedure derives the emissivity spectrum and the temperature of the target adopting the maximum entropy (MaxEnt) estimation approach. The main advantage of the MaxEnt statistical inference is the absence of any external hypothesis, which is, instead, the main critical point characterizing any other temperature-emissivity separation (TES) algorithm. The MaxEnTES algorithm carries out the TES task adopting a modified version of the subgradient Shor's r-algorithm adopted for numerical optimization of a MaxEnt objective function. For this purpose, we have utilized the C/C++ Solvopt code from the University of Gratz to develop a practical data processing implementation. In this paper, we discuss the mathematical structure of the MaxEnTES algorithm and analyze its performance in depth using numerical simulations and remote sensing Multispectral Infrared/Visible Imaging Spectrometer images. We show that the MaxEnTES algorithm provides improved accuracy for temperature and emissivity estimation, lowering the standard estimation error to a fraction of degree Kelvin. In agreement with previous investigations, we find that the estimation accuracy grows when increasing the number of available spectral channels. The systematic errors affecting the temperature estimates (e.g., bias) are thoroughly evaluated. We prove that the MaxEnTES algorithm retrieves the correct shape of the target emissivity spectrum even in presence of a significant temperature estimation error.