  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 super-resolution algorithm first proposed in the context of
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.
