In this research study, we deal with remote sensing data analysis over high dimensional space formed by hyperspectral images. This task is generally complex due to the large spectral, spatial richness, and mixed pixels. Thus, several spectral un-mixing methods have been proposed to discriminate mixing spectra by estimating the classes and their presence rates. However, information related to mixed pixel composition is very interesting for some applications, but it is insufficient for many others. Thus, it is necessary to have much more data about the spatial localization of the classes detected during the spectral un-mixing process. To solve the above-mentioned problem and specify the spatial location of the different land cover classes in the mixed pixel, sub-pixel mapping techniques were introduced. This manuscript presents a novel sub-pixel mapping process relying on K-SVD (K-singular value decomposition) learning and total variation as a spatial regularization parameter (SMKSVD-TV: Sub-pixel Mapping based on K-SVD dictionary learning and Total Variation). The proposed approach adopts total variation as a spatial regularization parameter, to make edges smooth, and a pre-constructed spatial dictionary with the K-SVD dictionary training algorithm to have more spatial configurations at the sub-pixel level. It was tested and validated with three real hyperspectral data. The experimental results reveal that the attributes obtained by utilizing a learned spatial dictionary with isotropic total variation allowed improving the classes sub-pixel spatial localization, while taking into account pre-learned spatial patterns. It is also clear that the K-SVD dictionary learning algorithm can be applied to construct a spatial dictionary, particularly for each data set.

International audienceWithin the framework of the unmixing of hyperspectral images, the pixel mixture is a difficult problem to solve. This difficulty comes from several outliers which seriously affect the reliability of spectral unmixing results. The illumination change effect, where the image does not reflect the true appearance of the scene, in many cases due to shadow facts, is considered to be one of the most important outliers. The present work proposes a new approach called Spectral Angle Measure-based Spectral Unmixing which uses the spectral angle constraint for abundance quantification. The major benefit of this approach is its ability to take advantage of the geometric properties of the Spectral Angle Measure technique to estimate abundance quantification independently of the amplitude (magnitude) of the Endmembers spectral signatures, using only spectral angle measures. As a consequence, a significant reduction in spectral unmixed error corresponding to the spectral similarity within-class confusion is obtained. A second benefit concerns physical constraints which are respected. The experiment was conducted using simulated and real images to validate our approach and to compare it with a well known statistical one

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