Total-Variation Mode Decomposition

Ido Cohen; Tom Berkov; Guy Gilboa

doi:10.1007/978-3-030-75549-2_5

Total-Variation Mode Decomposition

Ido Cohen, Tom Berkov, Guy Gilboa

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

In this work we analyze the Total Variation (TV) flow applied to one dimensional signals. We formulate a relation between Dynamic Mode Decomposition (DMD), a dimensionality reduction method based on the Koopman operator, and the spectral TV decomposition. DMD is adapted by time rescaling to fit linearly decaying processes, such as the TV flow. For the flow with finite subgradient transitions, a closed form solution of the rescaled DMD is formulated. In addition, a solution to the TV-flow is presented, which relies only on the initial condition and its corresponding subgradient. A very fast numerical algorithm is obtained which solves the entire flow by elementary subgradient updates.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings
Editors	Abderrahim Elmoataz, Jalal Fadili, Yvain Quéau, Julien Rabin, Loïc Simon
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	52-64
Number of pages	13
ISBN (Print)	9783030755485
DOIs	https://doi.org/10.1007/978-3-030-75549-2_5
State	Published - 2021
Externally published	Yes
Event	8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021 - Virtual, Online Duration: 16 May 2021 → 20 May 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12679 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021
City	Virtual, Online
Period	16/05/21 → 20/05/21

Keywords

Dynamic Mode Decomposition
Time reparametrization
Total Variation-flow
Total Variation-spectral decomposition

Access to Document

10.1007/978-3-030-75549-2_5

Cite this

Cohen, I., Berkov, T., & Gilboa, G. (2021). Total-Variation Mode Decomposition. In A. Elmoataz, J. Fadili, Y. Quéau, J. Rabin, & L. Simon (Eds.), Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings (pp. 52-64). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12679 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-75549-2_5

Cohen, Ido ; Berkov, Tom ; Gilboa, Guy. / Total-Variation Mode Decomposition. Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings. editor / Abderrahim Elmoataz ; Jalal Fadili ; Yvain Quéau ; Julien Rabin ; Loïc Simon. Springer Science and Business Media Deutschland GmbH, 2021. pp. 52-64 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In this work we analyze the Total Variation (TV) flow applied to one dimensional signals. We formulate a relation between Dynamic Mode Decomposition (DMD), a dimensionality reduction method based on the Koopman operator, and the spectral TV decomposition. DMD is adapted by time rescaling to fit linearly decaying processes, such as the TV flow. For the flow with finite subgradient transitions, a closed form solution of the rescaled DMD is formulated. In addition, a solution to the TV-flow is presented, which relies only on the initial condition and its corresponding subgradient. A very fast numerical algorithm is obtained which solves the entire flow by elementary subgradient updates.",

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Cohen, I, Berkov, T & Gilboa, G 2021, Total-Variation Mode Decomposition. in A Elmoataz, J Fadili, Y Quéau, J Rabin & L Simon (eds), Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12679 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 52-64, 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021, Virtual, Online, 16/05/21. https://doi.org/10.1007/978-3-030-75549-2_5

Total-Variation Mode Decomposition. / Cohen, Ido; Berkov, Tom; Gilboa, Guy.
Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings. ed. / Abderrahim Elmoataz; Jalal Fadili; Yvain Quéau; Julien Rabin; Loïc Simon. Springer Science and Business Media Deutschland GmbH, 2021. p. 52-64 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12679 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - In this work we analyze the Total Variation (TV) flow applied to one dimensional signals. We formulate a relation between Dynamic Mode Decomposition (DMD), a dimensionality reduction method based on the Koopman operator, and the spectral TV decomposition. DMD is adapted by time rescaling to fit linearly decaying processes, such as the TV flow. For the flow with finite subgradient transitions, a closed form solution of the rescaled DMD is formulated. In addition, a solution to the TV-flow is presented, which relies only on the initial condition and its corresponding subgradient. A very fast numerical algorithm is obtained which solves the entire flow by elementary subgradient updates.

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Cohen I, Berkov T, Gilboa G. Total-Variation Mode Decomposition. In Elmoataz A, Fadili J, Quéau Y, Rabin J, Simon L, editors, Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 52-64. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-75549-2_5

Total-Variation Mode Decomposition

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Keywords

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