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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 {\it 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.

65K10Optimization techniques (numerical methods)
49J20Optimal control problems with PDE (existence)
49M25Discrete approximations in calculus of variations
49M29Methods involving duality in calculus of variations
Full Text: DOI
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