This paper presents a new approach to post temperature and emissivity separation processing for thermal infrared hyperspectral remote sensing data, based upon sparse signal representation. We address the denoising of emissivity product, where the atmospheric correction error, temperature and emissivty separation error and data noise are to be removed from a given emissivity product. The approach taken is based on a hypothesis of redundancy that among emissivity spectrum of features with common end-member components has strong spectral redundancy, then we can recover the emissivity spectrum based upon Sparse Representation (SR). Using the K-SVD algorithm and a priori spectral library data, we obtain a dictionary that describes the features emissivity spectrum content effectively. We show how such approach leads to a simple and effective spectra denoising that correct the retrieved emissivity close to real value.