First-order geometric multilevel optimization for discrete tomography

0542259 - ÚTIA 2022 RIV CH eng C - Conference Paper (international conference)
Plier, J. - Savarino, F. - Kočvara, Michal - Petra, S.
First-order geometric multilevel optimization for discrete tomography.
Scale Space and Variational Methods in Computer Vision: 8th International Conference, SSVM 2021. Cham: Springer, 2021, s. 191-203. Lecture Notes in Computer Science, 12679. ISBN 978-3-030-75549-2.
[International Conference on Scale Space and Variational Methods in Computer Vision : SSVM 2021 /8./. Virtual Event (CH), 16.05.2021-20.05.2021]
Institutional support: RVO:67985556
Keywords : discrete tomography * multilevel optimization * n-orthotope
OECD category: Applied mathematics
http://library.utia.cas.cz/separaty/2021/MTR/kocvara-0542259.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0320772