A variable splitting augmented Lagrangian approach to linear spectral unmixing

• Published in: 2009 First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing pp. 1 - 4
• Main Author: Bioucas-Dias, J.M.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.08.2009
• Subjects: Additive noise; Constraint optimization; Hyperspectral imaging; Hyperspectral unmixing; Lagrangian functions; Minimum volume simplex; Noise robustness; nonsmooth optimization; Solid modeling; Source separation; Telecommunications; Variable Splitting augmented Lagrangian; Vectors
• ISBN: 9781424446865; 1424446864
• ISSN: 2158-6268
• DOI: 10.1109/WHISPERS.2009.5289072

This paper presents a new linear hyperspectral unmixing method of the minimum volume class, termed simplex identification via split augmented Lagrangian (SISAL). Following Craig's seminal ideas, hyperspectral linear unmixing amounts to finding the minimum volume simplex containing the hyperspectral vectors. This is a nonconvex optimization problem with convex constraints. In the proposed approach, the positivity constraints, forcing the spectral vectors to belong to the convex hull of the end member signatures, are replaced by soft constraints. The obtained problem is solved by a sequence of augmented Lagrangian optimizations. The resulting algorithm is very fast and able so solve problems far beyond the reach of the current state-of-the art algorithms. The effectiveness of SISAL is illustrated with simulated data.