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Comparison of formulations and solution methods for image restoration problems. (English) Zbl 1016.94004
The aim of the paper is to analyse and compare different formulations and their solution methods for image restoration (denoising) problems. 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 is proposed and analysed.

MSC:
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49J52 Nonsmooth analysis
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