TY - GEN
T1 - Total-Variation Mode Decomposition
AU - Cohen, Ido
AU - Berkov, Tom
AU - Gilboa, Guy
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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.
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.
KW - Dynamic Mode Decomposition
KW - Time reparametrization
KW - Total Variation-flow
KW - Total Variation-spectral decomposition
UR - http://www.scopus.com/inward/record.url?scp=85106441260&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-75549-2_5
DO - 10.1007/978-3-030-75549-2_5
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AN - SCOPUS:85106441260
SN - 9783030755485
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 52
EP - 64
BT - Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings
A2 - Elmoataz, Abderrahim
A2 - Fadili, Jalal
A2 - Quéau, Yvain
A2 - Rabin, Julien
A2 - Simon, Loïc
PB - Springer Science and Business Media Deutschland GmbH
T2 - 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021
Y2 - 16 May 2021 through 20 May 2021
ER -