Comparison of formulations and solution methods for image restoration problems

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Abstract
Different formulations for image restoration problems are presented, analysed and compared. Two of the three formulations considered are smooth enough to satisfy the assumptions for convergence of ordinary gradient-based optimization methods, such as the conjugate gradient method. For solving the third problem, two general methods of nonsmooth optimization are applied: a (first-order) proximal bundle method and a (second-order) bundle-Newton method. Moreover, a new generalization of active-set methods that have earlier shown high efficiency for BV-regularized image restoration problems is proposed and analysed. Comparison of methods as well as different formulations is completed with numerical experiments.

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