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Aiming at low spectral contrast materials, the Optimized Smoothing for Temperature Emissivity Separation (OSTES) method was developed to improve the Temperature and Emissivity Separation (TES) algorithm based on the linear relationship between brightness temperature and emissivity features, but there was little smoothing improvement for higher spectral contrast materials. In this paper, a new nonlinear-relationship based algorithm is presented, focusing on improving the performance of the OSTES method for materials with middle or high spectral contrast. This novel approach is a two-step procedure. Firstly, by introducing atmospheric impact factor, the nonlinear relationship is mathematically proved using first-order Taylor series approximation. Moreover, it is proven that nonlinear model has stronger universality than linear model. Secondly, a new method named Temperature and Emissivity Separation with Nonlinear Constraint (TESNC) is proposed based on the nonlinear model for smoothing temperature and emissivity retrieval. The key procedure of TESNC is the lowest emissivity smoothing estimation based on nonlinear model and retrieved by minimizing the reconstruction error of the Planck radiance. TESNC was tested on a series of synthetic data with different kinds of natural materials representing several multispectral and hyperspectral infrared sensors. It is shown that, especially for materials with higher spectral contrast, the proposed method is less sensitive to changes in atmospheric conditions and sample temperatures. Furthermore, the standard Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) products in different kind of atmospheric conditions were used for verifying the improvement. TESNC is more accurate and stable with the decrease of emissivity and changes of atmospheric conditions compared with TES, Adjusted Normalized Emissivity Method (ANEM), and OSTES methods.

Temperature and Emissivity Smoothing Separation with Nonlinear Relation of Brightness Temperature and Emissivity for Thermal Infrared Sensors