Total variation regulatization in sparse hyperspectral unmixing

Hyperspectral unmixing has recently been addressed as a sparse regression problem by using predefined spectral libraries instead of image-derived endmembers in the unmixing process. This new approach has attracted much attention, as it sidesteps well known obstacles met in endmember extraction, such as the stopping criteria for the extraction process (represented by the number of endmembers needed to explain the observed scene) and the fact that the scene might not contain pure pixels. It happens, however, that in many applications the spectral libraries contain highly correlated signatures, which limits the success of sparse regression applied to mixtures with a very small number of materials. In this paper, we mitigate this limitation by adding the total variation regularization to the classical sparse regression, thus, exploiting the spatial contextual information present in the hyperspectral images. The effectiveness of the new approach is illustrated in experiments carried out on simulated data sets.