A temperature and emissivity separation algorithm based on maximum entropy estimation of alpha spectrum's scaling and translation

Abstract

In the thermal infrared (TIR) waveband, solving the target emissivity spectrum and temperature leads to an ill-posed problem in which the number of unknown parameters is larger than that of available measurements. Generally, the approaches developed for solving this kind of problems are called, by a joint name, the TES (temperature and emissivity separation) algorithm. As is shown in the name, the TES algorithm is dedicated to separating the target temperature and emissivity in the calculating procedure. In this paper, a novel method called the new MaxEnt (maximum entropy) TES algorithm is proposed, which is considered as a promotion of the MaxEnt TES algorithm proposed by Barducci. The maximum entropy estimation is utilized as the basic framework in the two preceding algorithms, so that the two algorithms both could make temperature and emissivity separation, independent of experiential information derived by some special data bases. As a result, the two algorithms could be applied to solve the temperature and emissivity spectrum of the targets which are absolutely unknown to us. However, what makes the two algorithms different is that the alpha spectrum derived by the ADE (alpha derived emissivity) method is considered as priori information to be added in the new MaxEnt TES algorithm. Based on the Wien approximation, the ADE method is dedicated to the calculation of the alpha spectrum which has a similar distribution to the true emissivity spectrum. Based on the preceding promotion, the new MaxEnt TES algorithm keeps a simpler mathematical formalism. Without any doubt, the new MaxEnt TES algorithm provides a faster computation for large volumes of data (i.e. hyperspectral images of the Earth). Some numerical simulations have been performed; the data and results show that, the maximum RMSE of emissivity estimation is 0.017, the maximum absolute error of temperature estimation is 0.62 K. Added with Gaussian white noise in which the signal to noise ratio is measured to be 11, the relative RMSE of emissivity estimation is 2.67%, the relative error of temperature estimation is 1.26%. Conclusion shows that the new MaxEnt TES algorithm may achieve high accuracy and fast calculating speed, and also get nice robustness against noise.