Riemannian geometry for inverse problems in cryogenic electron microscopy
type: CreativeWork
description: This thesis develops theory and algorithms for a Riemannian geometric approach to inverse problems in cryogenic electron microscopy (Cryo-EM). It is divided into two parts, motivated by the sub problem of orientation estimation and that of modelling of protein dynamics. The thesis is concluded with a discussion on how to bring these pieces together to solve the so-called continuous heterogeneous reconstruction problem and a reflection on the general implications and new opportunities that a Riemannian geometry-based approach has for and brings to signal processing and recovery problems. In the first part of the thesis we consider how to use ideas from global optimisation on Riemannian manifolds to regularise the orientation estimation sub problem. Our approach is motivated by the two main challenges in orientation estimation: the high noise levels present in Cryo-EM data and the non-convexity of typical variational problems for estimating orientations. To overcome these challenges jointly, we construct a new regularised global optimisation scheme to solve a variational problem for orientation estimation in a more noise-robust fashion. In the second (and main) part we focus on constructing a Riemannian manifold for protein conformations. In particular, we are interested in constructing Riemannian geometry for protein conformations such that physically realistic protein conformations live in low-dimensional geodesic subspaces. Before constructing a Riemannian manifold, we first consider how curvature causes a discrepancy between data only looking low-dimensional and data actually being low-dimensional, and also consider how to address such curvature effects. Next, we construct a Riemannian manifold of protein conformations with computationally feasible manifold mappings such that realistic protein dynamics data really are low-dimensional under the proposed Riemannian structure, i.e., not suffering from curvature effects. Thirdly, we argue that it could be beneficial t…
abstract: This thesis develops theory and algorithms for a Riemannian geometric approach to inverse problems in cryogenic electron microscopy (Cryo-EM). It is divided into two parts, motivated by the sub problem of orientation estimation and that of modelling of protein dynamics. The thesis is concluded with a discussion on how to bring these pieces together to solve the so-called continuous heterogeneous reconstruction problem and a reflection on the general implications and new opportunities that a Riemannian geometry-based approach has for and brings to signal processing and recovery problems. In the first part of the thesis we consider how to use ideas from global optimisation on Riemannian manifolds to regularise the orientation estimation sub problem. Our approach is motivated by the two main challenges in orientation estimation: the high noise levels present in Cryo-EM data and the non-convexity of typical variational problems for estimating orientations. To overcome these challenges jointly, we construct a new regularised global optimisation scheme to solve a variational problem for orientation estimation in a more noise-robust fashion. In the second (and main) part we focus on constructing a Riemannian manifold for protein conformations. In particular, we are interested in constructing Riemannian geometry for protein conformations such that physically realistic protein conformations live in low-dimensional geodesic subspaces. Before constructing a Riemannian manifold, we first consider how curvature causes a discrepancy between data only looking low-dimensional and data actually being low-dimensional, and also consider how to address such curvature effects. Next, we construct a Riemannian manifold of protein conformations with computationally feasible manifold mappings such that realistic protein dynamics data really are low-dimensional under the proposed Riemannian structure, i.e., not suffering from curvature effects. Thirdly, we argue that it could be beneficial t…
author: Diepeveen, Willem
language: eng
keywords: cryogenic electron microscopy, manifold-valued data, Riemannian manifold
license: https://www.repository.cam.ac.uk/bitstreams/439f26f8-8792-4f6a-afa7-7443a5ffbb7f/download
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
date published: 2024-04-09
date modified: 2026-07-22T22:23:54Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.109508