Emissivity spectra estimated with the MaxEnTES algorithm

Abstract

Temperature and Emissivity Separation (TES) applied to multispectral or hyperspectral Thermal Infrared (TIR) images of the Earth is a relevant issue for many remote sensing applications. The TIR spectral radiance can be modeled by means of the well-known Planck’s law, as a function of the target temperature and emissivity. The estimation of these target's parameters (i.e. the Temperature Emissivity Separation, aka TES) is hindered by the circumstance that the number of measurements is less than the unknown number. Existing TES algorithms implement a temperature estimator in which the uncertainty is removed by adopting some a priori assumption that conditions the retrieved temperature and emissivity. Due to its mathematical structure, the Maximum Entropy formalism (MaxEnt) seems to be well suited for carrying out this complex TES operation. The main advantage of the MaxEnt statistical inference is the absence of any external hypothesis, which is instead characterizes most of the existing the TES algorithms. In this paper we describe the performance of the MaxEnTES (Maximum Entropy Temperature Emissivity Separation) algorithm as applied to ten TIR spectral channels of a MIVIS dataset collected over Italy. We compare the temperature and emissivity spectra estimated by this algorithm with independent estimations achieved with two previous TES methods (the Grey Body Emissivity (GBE), and the Model Emittance Calculation (MEC)). We show that MaxEnTES is a reliable algorithm in terms of its higher output Signal-to-Noise Ratio and the negligibility of systematic errors that bias the estimated temperature in other TES procedures.