First-order geometric multilevel optimization for discrete tomography

Jan Plier; Fabrizio Savarino; Michal Kocvara; Stefania Petra

doi:10.1007/978-3-030-75549-2_16

First-order geometric multilevel optimization for discrete tomography

Jan Plier, Fabrizio Savarino, Michal Kocvara, Stefania Petra

Mathematics

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

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Abstract

Discrete tomography (DT) naturally leads to a hierarchy of models of varying discretization levels. We employ multilevel optimization (MLO) to take advantage of this hierarchy: while working at the fine level we compute the search direction based on a coarse model. Importing concepts from information geometry to the n-orthotope, we propose a smoothing operator that only uses first-order information and incorporates constraints smoothly. We show that the proposed algorithm is well suited to the ill-posed reconstruction problem in DT, compare it to a recent MLO method that nonsmoothly incorporates box constraints and demonstrate its efficiency on several large-scale examples.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision
Subtitle of host publication	8th International Conference, SSVM 2021, Virtual Event, May 16–20, 2021, Proceedings
Editors	A Elmoataz, J Fadili, Y Queau, J Rabin, L Simon
Publisher	Springer
Pages	191-203
ISBN (Electronic)	9783030755492
ISBN (Print)	9783030755485
DOIs	https://doi.org/10.1007/978-3-030-75549-2_16
Publication status	Published - 30 Apr 2021
Event	SSVM 2021: Scale Space and Variational Methods in Computer Vision - Duration: 16 May 2021 → 20 May 2021

Publication series

Name	Lecture Notes in Computer Science
Volume	12679
ISSN (Print)	0302-9743

Conference

Conference	SSVM 2021: Scale Space and Variational Methods in Computer Vision
Abbreviated title	SSVM 2021
Period	16/05/21 → 20/05/21

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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The final authenticated version is available online at https://doi.org/10.1007/978-3-030-75549-2_16.
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Plier, J., Savarino, F., Kocvara, M., & Petra, S. (2021). First-order geometric multilevel optimization for discrete tomography. In A. Elmoataz, J. Fadili, Y. Queau, J. Rabin, & L. Simon (Eds.), Scale Space and Variational Methods in Computer Vision: 8th International Conference, SSVM 2021, Virtual Event, May 16–20, 2021, Proceedings (pp. 191-203). (Lecture Notes in Computer Science; Vol. 12679). Springer. https://doi.org/10.1007/978-3-030-75549-2_16

Plier, Jan ; Savarino, Fabrizio ; Kocvara, Michal et al. / First-order geometric multilevel optimization for discrete tomography. Scale Space and Variational Methods in Computer Vision: 8th International Conference, SSVM 2021, Virtual Event, May 16–20, 2021, Proceedings. editor / A Elmoataz ; J Fadili ; Y Queau ; J Rabin ; L Simon. Springer, 2021. pp. 191-203 (Lecture Notes in Computer Science).

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title = "First-order geometric multilevel optimization for discrete tomography",

abstract = "Discrete tomography (DT) naturally leads to a hierarchy of models of varying discretization levels. We employ multilevel optimization (MLO) to take advantage of this hierarchy: while working at the fine level we compute the search direction based on a coarse model. Importing concepts from information geometry to the n-orthotope, we propose a smoothing operator that only uses first-order information and incorporates constraints smoothly. We show that the proposed algorithm is well suited to the ill-posed reconstruction problem in DT, compare it to a recent MLO method that nonsmoothly incorporates box constraints and demonstrate its efficiency on several large-scale examples.",

author = "Jan Plier and Fabrizio Savarino and Michal Kocvara and Stefania Petra",

year = "2021",

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doi = "10.1007/978-3-030-75549-2_16",

language = "English",

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editor = "A Elmoataz and J Fadili and Queau, {Y } and J Rabin and L Simon",

booktitle = "Scale Space and Variational Methods in Computer Vision",

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Plier, J, Savarino, F, Kocvara, M & Petra, S 2021, First-order geometric multilevel optimization for discrete tomography. in A Elmoataz, J Fadili, Y Queau, J Rabin & L Simon (eds), Scale Space and Variational Methods in Computer Vision: 8th International Conference, SSVM 2021, Virtual Event, May 16–20, 2021, Proceedings. Lecture Notes in Computer Science, vol. 12679, Springer, pp. 191-203, SSVM 2021: Scale Space and Variational Methods in Computer Vision, 16/05/21. https://doi.org/10.1007/978-3-030-75549-2_16

First-order geometric multilevel optimization for discrete tomography. / Plier, Jan; Savarino, Fabrizio; Kocvara, Michal et al.
Scale Space and Variational Methods in Computer Vision: 8th International Conference, SSVM 2021, Virtual Event, May 16–20, 2021, Proceedings. ed. / A Elmoataz; J Fadili; Y Queau; J Rabin; L Simon. Springer, 2021. p. 191-203 (Lecture Notes in Computer Science; Vol. 12679).

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

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T1 - First-order geometric multilevel optimization for discrete tomography

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AU - Petra, Stefania

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N2 - Discrete tomography (DT) naturally leads to a hierarchy of models of varying discretization levels. We employ multilevel optimization (MLO) to take advantage of this hierarchy: while working at the fine level we compute the search direction based on a coarse model. Importing concepts from information geometry to the n-orthotope, we propose a smoothing operator that only uses first-order information and incorporates constraints smoothly. We show that the proposed algorithm is well suited to the ill-posed reconstruction problem in DT, compare it to a recent MLO method that nonsmoothly incorporates box constraints and demonstrate its efficiency on several large-scale examples.

AB - Discrete tomography (DT) naturally leads to a hierarchy of models of varying discretization levels. We employ multilevel optimization (MLO) to take advantage of this hierarchy: while working at the fine level we compute the search direction based on a coarse model. Importing concepts from information geometry to the n-orthotope, we propose a smoothing operator that only uses first-order information and incorporates constraints smoothly. We show that the proposed algorithm is well suited to the ill-posed reconstruction problem in DT, compare it to a recent MLO method that nonsmoothly incorporates box constraints and demonstrate its efficiency on several large-scale examples.

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BT - Scale Space and Variational Methods in Computer Vision

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A2 - Fadili, J

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Plier J, Savarino F, Kocvara M, Petra S. First-order geometric multilevel optimization for discrete tomography. In Elmoataz A, Fadili J, Queau Y, Rabin J, Simon L, editors, Scale Space and Variational Methods in Computer Vision: 8th International Conference, SSVM 2021, Virtual Event, May 16–20, 2021, Proceedings. Springer. 2021. p. 191-203. (Lecture Notes in Computer Science). doi: 10.1007/978-3-030-75549-2_16

First-order geometric multilevel optimization for discrete tomography

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