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Spectral unmixing and sub-pixel mapping have been used to estimate the proportion and spatial distribution of the different land-cover classes in mixed pixels at a sub-pixel scale. In the past decades, several algorithms were proposed in both categories; however, these two techniques are generally regarded as independent procedures, with most sub-pixel mapping methods using abundance maps generated by spectral unmixing techniques. It should be noted that the utilized abundance map has a strong impact on the performance of the subsequent sub-pixel mapping process. Recently, we built a novel sub-pixel mapping model in combination with the linear spectral mixture model. Therefore, a joint sub-pixel mapping model was established that connects an original (coarser resolution) remotely sensed image with the final sub-pixel result directly. However, this approach focuses on incorporating the spectral information contained in the original image without addressing the spectral endmember variability resulting from variable illumination and environmental conditions. To address this important issue, in this paper we designed a new joint sparse sub-pixel mapping method under the assumption that various representative spectra for each endmember are known a priori and available in a library. In addition, the total variation (TV) regularization was also adopted to exploit the spatial information. The proposed approach was experimentally evaluated using both synthetic and real hyperspectral images, and the obtained results demonstrate that the method can achieve better results by considering the impact of endmember variability when compared with other sub-pixel mapping methods

Joint Sparse Sub-Pixel Mapping Model with Endmember Variability for Remotely Sensed Imagery