SparseAlign: A Grid-Free Algorithm for Automatic Marker Localization and Deformation Estimation in Cryo-Electron Tomography

IEEE Transactions on Computational Imaging, vol. 8, pp. 651–665

Abstract

Tilt-series alignment is crucial to obtaining high-resolution reconstructions in cryo-electron tomography. Beam-induced local deformation of the sample is hard to estimate from the low-contrast sample alone, and often requires fiducial gold bead markers. The state-of-the-art approach for deformation estimation uses (semi-)manually labelled marker locations in projection data to fit the parameters of a polynomial deformation model. Manually-labelled marker locations are difficult to obtain when data are noisy or markers overlap in projection data. We propose an alternative mathematical approach for simultaneous marker localization and deformation estimation by extending a grid-free algorithm first proposed in the context of super-resolution single-molecule localization microscopy. Our approach does not require labelled marker locations; instead, we use an image-based loss where we compare the forward projection of markers with the observed data. We equip this marker localization scheme with an additional deformation estimation component and solve for a reduced number of deformation parameters. Using extensive numerical studies on marker-only samples, we show that our approach automatically finds markers and reliably estimates sample deformation without labelled marker data. We further demonstrate the applicability of our approach for a broad range of model mismatch scenarios, including experimental electron tomography data of gold markers on ice.

Authors 6

1. Poulami Somanya Ganguly Aachen Mathematical Institute

   Leiden University · Centrum Wiskunde & Informatica

   Affiliation as printed

   Computational Imaging, Centrum Wiskunde and Informatica, Amsterdam, XG, The Netherlands

   Mathematical Institute, Leiden University, Leiden, The Netherlands

2. Felix F. Lucka

   Centrum Wiskunde & Informatica

   Affiliation as printed

   Computational Imaging Group, Centrum Wiskunde and Informatica, Amsterdam, XG, The Netherlands

3. Holger Kohr

   Thermo Fisher Scientific (Netherlands)

   Affiliation as printed

   Thermo Fisher Scientific, Eindhoven, The Netherlands

4. Erik Franken

   Thermo Fisher Scientific (Netherlands)

   Affiliation as printed

   Thermo Fisher Scientific, Eindhoven, The Netherlands

5. Hermen Jan Hupkes Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, Leiden, EZ, The Netherlands

6. Kees Joost Batenburg Aachen Leiden Institute of Advanced Computer Science

   Leiden University · Centrum Wiskunde & Informatica

   Affiliation as printed

   Computational Imaging, Centrum Wiskunde and Informatica, Amsterdam, XG, The Netherlands

   Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands