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Hyperspectral analysis has gained popularity over recent years as a way toinfer what materials are displayed on a picture whose pixels consist of amixture of spectral signatures. Computing both signatures and mixturecoefficients is known as unsupervised unmixing, a set of techniques usuallybased on non-negative matrix factorization. Unmixing is a difficult non-convexproblem, and algorithms may converge to one out of many local minima, which maybe far removed from the true global minimum. Computing this true minimum isNP-hard and seems therefore out of reach. Aiming for interesting local minima,we investigate the addition of total variation regularization terms. Advantagesof these regularizers are two-fold. Their computation is typically ratherlight, and they are deemed to preserve sharp edges in pictures. This paperdescribes an algorithm for regularized hyperspectral unmixing based on theAlternating Direction Method of Multipliers.

Total variation regularized non-negative matrix factorization for smooth hyperspectral unmixing