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

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.

A computationally efficient reconstruction algorithm for circular cone-beam computed tomography using shallow neural networks

Circular cone-beam (CCB) Computed Tomography (CT) has become an integral part of industrial quality control, materials science and medical imaging. The need to acquire and process each scan in a short time naturally leads to trade-offs between speed and reconstruction quality, creating a need for fast reconstruction algorithms capable of creating accurate reconstructions from limited data. In this paper we introduce the Neural Network Feldkamp-Davis-Kress (NN-FDK) algorithm. This algorithm adds a machine learning component to the FDK algorithm to improve its reconstruction accuracy while maintaining its computational efficiency. Moreover, the NN-FDK algorithm is designed such that it has low training data requirements and is fast to train. This ensures that the proposed algorithm can be used to improve image quality in high throughput CT scanning settings, where FDK is currently used to keep pace with the acquisition speed using readily available computational resources. We compare the NN-FDK algorithm to two standard CT reconstruction algorithms and to two popular deep neural networks trained to remove reconstruction artifacts from the 2D slices of an FDK reconstruction. We show that the NN-FDK reconstruction algorithm is substantially faster in computing a reconstruction than all the tested alternative methods except for the standard FDK algorithm and we show it can compute accurate CCB CT reconstructions in cases of high noise, a low number of projection angles or large cone angles. Moreover, we show that the training time of an NN-FDK network is orders of magnitude lower than the considered deep neural networks, with only a slight reduction in reconstruction accuracy.