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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.16879 |
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| _version_ | 1866916279117414400 |
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| author | Muller, Tommi Duncan, Adriana L. Verbeke, Eric J. Kileel, Joe |
| author_facet | Muller, Tommi Duncan, Adriana L. Verbeke, Eric J. Kileel, Joe |
| contents | We revisit the topic of common lines between projection images in single particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain $2n \times n$ matrix storing properly-scaled basis vectors for the common lines between $n$ projection images of one molecular conformation. Using this algebraic constraint and others, we give optimization algorithms to denoise common lines and recover the unknown 3D rotations associated to the images. As an application, we develop a clustering algorithm to partition a set of noisy images into homogeneous communities using common lines, in the case of discrete heterogeneity in cryo-EM. We demonstrate the methods on synthetic and experimental datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16879 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic Constraints and Algorithms for Common Lines in Cryo-EM Muller, Tommi Duncan, Adriana L. Verbeke, Eric J. Kileel, Joe Optimization and Control Algebraic Geometry 90C26, 14Q30 We revisit the topic of common lines between projection images in single particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain $2n \times n$ matrix storing properly-scaled basis vectors for the common lines between $n$ projection images of one molecular conformation. Using this algebraic constraint and others, we give optimization algorithms to denoise common lines and recover the unknown 3D rotations associated to the images. As an application, we develop a clustering algorithm to partition a set of noisy images into homogeneous communities using common lines, in the case of discrete heterogeneity in cryo-EM. We demonstrate the methods on synthetic and experimental datasets. |
| title | Algebraic Constraints and Algorithms for Common Lines in Cryo-EM |
| topic | Optimization and Control Algebraic Geometry 90C26, 14Q30 |
| url | https://arxiv.org/abs/2403.16879 |