基于最大熵估计Alpha谱缩放与平移量的温度与发射率分离算法

在热红外波段, 为了使温度与发射率分离过程不依赖数据库提供的经验信息, 并且实现更高的反演精度和更快的计算速度, 研究了一种新的温度与发射率分离算法. 首先, 在维恩近似原理的基础上, 求解了Alpha谱分布, 并利用Alpha谱描述光谱发射率的形状信息. 其次, 改进了最大熵温度与发射率分离算法: 应用最大熵估计模型对Alpha谱缩放与平移量进行估计, 减少了待估计参数的数量, 大幅简化了求解过程. 最后, 进行了算法的数值仿真实验: 求解了典型地物目标的温度与光谱发射率, 并且分析了算法对系统噪声的鲁棒性. 仿真数据表明: 发射率估计的最大RMSE为0.017, 温度估计的最大绝对误差的绝对值为0.62 K; 对系统添加测量信噪比为11的高斯白噪声, 发射率估计的相对RMSE为2.67%, 温度估计的相对误差为1.26%. 结果表明: 本文所述算法求解精度高, 计算速度快, 具备良好的鲁棒性.

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

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.