This paper presents a new linear hyperspectral unmixing method of the minimumvolume class, termed \emph{simplex identification via split augmentedLagrangian} (SISAL). Following Craig's seminal ideas, hyperspectral linearunmixing amounts to finding the minimum volume simplex containing thehyperspectral vectors. This is a nonconvex optimization problem with convexconstraints. In the proposed approach, the positivity constraints, forcing thespectral vectors to belong to the convex hull of the endmember signatures, arereplaced by soft constraints. The obtained problem is solved by a sequence ofaugmented Lagrangian optimizations. The resulting algorithm is very fast andable so solve problems far beyond the reach of the current state-of-the artalgorithms. The effectiveness of SISAL is illustrated with simulated data.
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