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A preconditioned Forward-Backward approach with application to large-scale nonconvex spectral unmixing problems

Abstract : Many inverse problems require to minimize a criterion being the sum of a non necessarily smooth function and a Lipschitz differentiable function. Such an optimization problem can be solved with the Forward-Backward algorithm which can be accelerated thanks to the use of variable metrics derived from the Majorize-Minimize principle. The convergence of this approach is guaranteed provided that the criterion satisfies some additional technical conditions. Combining this method with an alternating minimization strategy will be shown to allow us to address a broad class of optimization problems involving large-size signals. An application example to a nonconvex spectral unmixing problem will be presented.
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https://hal.archives-ouvertes.fr/hal-01077329
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Audrey Repetti, Emilie Chouzenoux, Jean-Christophe Pesquet. A preconditioned Forward-Backward approach with application to large-scale nonconvex spectral unmixing problems. 39th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2014)., May 2014, Florence, Italy. pp.1498 - 1502, ⟨10.1109/ICASSP.2014.6853847⟩. ⟨hal-01077329⟩

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