A Total Variation Based Regularizer Promoting Piecewise-Lipschitz Reconstructions

Burger M, Korolev Y, Schönlieb CB, Stollenwerk C (2019)

Publication Type: Conference contribution

Publication year: 2019

Journal

Lecture Notes in Computer Science Springer Verlag

Publisher: Springer Verlag

Book Volume: 11603 LNCS

Pages Range: 485-497

Conference Proceedings Title: Lecture Notes in Computer Science

Event location: Hofgeismar DE

ISBN: 9783030223670

DOI: 10.1007/978-3-030-22368-7_38

Abstract

We introduce a new regularizer in the total variation family that promotes reconstructions with a given Lipschitz constant (which can also vary spatially). We prove regularizing properties of this functional and investigate its connections to total variation and infimal convolution type regularizers (Formula Presented) and, in particular, establish topological equivalence. Our numerical experiments show that the proposed regularizer can achieve similar performance as total generalized variation while having the advantage of a very intuitive interpretation of its free parameter, which is just a local estimate of the norm of the gradient. It also provides a natural approach to spatially adaptive regularization.

Authors with CRIS profile

Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

University of Cambridge GB United Kingdom (GB) Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE)

How to cite

APA:

Burger, M., Korolev, Y., Schönlieb, C.B., & Stollenwerk, C. (2019). A Total Variation Based Regularizer Promoting Piecewise-Lipschitz Reconstructions. In Jan Lellmann, Jan Modersitzki, Martin Burger (Eds.), Lecture Notes in Computer Science (pp. 485-497). Hofgeismar, DE: Springer Verlag.

MLA:

Burger, Martin, et al. "A Total Variation Based Regularizer Promoting Piecewise-Lipschitz Reconstructions." Proceedings of the 7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019, Hofgeismar Ed. Jan Lellmann, Jan Modersitzki, Martin Burger, Springer Verlag, 2019. 485-497.

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