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.

翻译：在低调样本中很难估计样本的本地化和变异性估算的替代数学方法,我们提议了一种替代的数学方法,用于同时标记本地化和变异性估算,方法是在单一分子局部化显微镜中首先提出的无网超级分辨率算法。 我们的方法并不要求标定标记位置;相反,我们使用基于图像的损失方法,将标记的远前预测与观察到的数据进行比较。我们用额外的变异性估计部分来为这一标记本地化计划配备额外的变异性估计部分,并解决变异参数数量减少的问题。我们使用仅使用标记的样本进行广泛的数字研究,我们显示我们的方法可以自动地找到一个广泛的标定标值和可靠标定的模型,以便进行我们用于进一步测试的标定标定的模型。