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Combined First and Second Order Variational Approaches for Image Processing

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Abstract

Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like image restoration, registration, segmentation, super-resolution, and estimation of flow fields. We review recent progress in mathematical image processing by combining first and second order derivatives in the regularization term of variational models. We demonstrate the power of the proposed methods by two rather different applications. The approaches make use of two different splitting methods of the functional to obtain iterative numerical schemes which require in each step only the computation of simple proximal mappings.

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Notes

  1. The scanning electron microscope tensile tests were performed at the Department of Mechanical and Process Engineering, University of Kaiserslautern by Dr. F. Balle, Prof. Dr. D. Eifler, and S. Schuff.

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Acknowledgement

Funding by the Deutsche Forschungsgemeinschaft (DFG) within the RTG GrK 1932 “Stochastic Models for Innovations in the Engineering Sciences”, project area P3, and within the DFG Grant STE571/11-1 is gratefully acknowledged.

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  1. Dept. of Mathematics, University of Kaiserslautern, Paul-Ehrlich-Str. 31, 67653, Kaiserslautern, Germany

    Gabriele Steidl

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Steidl, G. Combined First and Second Order Variational Approaches for Image Processing. Jahresber. Dtsch. Math. Ver. 117, 133–160 (2015). https://doi.org/10.1365/s13291-015-0113-2

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