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Regularizing Orientation Estimation in Cryogenic Electron Microscopy Three-Dimensional Map Refinement through Measure-Based Lifting over Riemannian Manifolds
Faculty of Mathematics, University of Cambridge, Cambridge, England.
Institute of Mathematics and Image Computing, University of Lubeck, Lubeck, Germany.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0002-1118-6483
Faculty of Mathematics, University of Cambridge, Cambridge, England.
2023 (English)In: SIAM Journal on Imaging Sciences, E-ISSN 1936-4954, Vol. 16, no 3, p. 1440-1490Article in journal (Refereed) Published
Abstract [en]

Motivated by the trade-off between noise robustness and data consistency for joint three-imensional (3D) map reconstruction and rotation estimation in single particle cryogenic-electron microscopy (Cryo-EM), we propose ellipsoidal support lifting (ESL), a measure-based lifting scheme for regularizing and approximating the global minimizer of a smooth function over a Riemannian manifold. Under a uniqueness assumption on the minimizer we show several theoretical results, in particular well-posedness of the method and an error bound due to the induced bias with respect to the global minimizer. Additionally, we use the developed theory to integrate the measure-based lifting scheme into an alternating update method for joint homogeneous 3D map reconstruction and rotation estimation, where typically tens of thousands of manifold-valued minimization problems have to be solved and where regularization is necessary because of the high noise levels in the data. The joint recovery method is used to test both the theoretical predictions and algorithmic performance through numerical experiments with Cryo-EM data. In particular, the induced bias due to the regularizing effect of ESL empirically estimates better rotations, i.e., rotations closer to the ground truth, than global optimization would.

Place, publisher, year, edition, pages
Society for Industrial & Applied Mathematics (SIAM) , 2023. Vol. 16, no 3, p. 1440-1490
Keywords [en]
cryo-electron microscopy, global optimization, nonconvex optimization, regularization, Riemannian optimization, rotation estimation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-341940DOI: 10.1137/22M1520773ISI: 001165605800004Scopus ID: 2-s2.0-85180366036OAI: oai:DiVA.org:kth-341940DiVA, id: diva2:1824793
Note

QC 20240301

Available from: 2024-01-08 Created: 2024-01-08 Last updated: 2024-04-25Bibliographically approved

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Öktem, Ozan

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