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A note on the dual treatment of higher-order regularization functionals. (English) Zbl 1087.65067
Summary: We apply the dual approach developed by A. Chambolle [J. Math. Imaging Vision 20, No. 1–2, 89–97 (2004)] for the Rudin-Osher-Fatemi model to regularization functionals with higher order derivatives. We emphasize the linear algebra point of view by consequently using matrix-vector notation. Numerical examples demonstrate the differences between various second order regularization approaches.
MSC:
65K10Optimization techniques (numerical methods)
49J20Optimal control problems with PDE (existence)
49M25Discrete approximations in calculus of variations
49M29Methods involving duality in calculus of variations
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