Inversion of emissivity spectrum and temperature in the TIR waveband based on the Maximum Entropy

• The Maximum Entropy estimation is used as the basic framework of this algorithm.
• The Alpha Spectrum or the Beta Spectrum is considered as a priori information.
• The method reconstructs the target emissivity spectrum and temperature.
• The method provides a faster computation for large volumes of data.

In the TIR (Thermal Infrared) waveband, solving the target emissivity spectrum and temperature leads to an ill-posed problem that the number of unknown parameters is more than the number 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. Regarded as a promotion of the MaxEnTES (Maximum Entropy TES) algorithm proposed by A. Barducci, a novel method called the New MaxEnTES algorithm is presented in this paper. The Maximum Entropy estimation is utilized to be the basic framework of each preceding algorithm. What makes the two algorithms different is that the Alpha Spectrum derived by ADE (Alpha Derived Emissivity method) or the Beta Spectrum derived by NEM (Normalized Emissivity Method) is considered as a priori information to be added in the New MaxEnTES algorithm. As a result, the New MaxEnTES algorithm keeps a simpler mathematical formalism. Without any doubt, the New MaxEnTES algorithm provides a faster computation for large volumes of data (i.e. hyperspectral images of the Earth). Some numerical simulations have been conducted to assess the performance of the New MaxEnTES algorithm. The results show that, the New MaxEnTES algorithm carefully reconstructs the target emissivity spectrum and temperature, and keeps the same orders of magnitude on accuracy with the MaxEnTES algorithm. What’s more, it also keeps good robust stabilization towards noise.