Principal component analysis (PCA) plays an important role in the analysis of cryo-electron microscopy (cryo-EM) images for various tasks such as classification, denoising, compression, and ab initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-EM projection images affected by radial point spread functions that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier–Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions. For $ N $ images of size $ L\times L $ , our method has time complexity $ O\left({NL}^3+{L}^4\right) $ and space complexity $ O\left({NL}^2+{L}^3\right) $ . In contrast to previous work, these complexities are independent of the number of different contrast transfer functions of the images. We demonstrate our approach on synthetic and experimental data and show acceleration by factors of up to two orders of magnitude.

Single-particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution three-dimensional (3D) structure of biological macromolecules from many noisy and randomly oriented projection images. One notable approach to 3D reconstruction, known as Kam’s method, relies on the moments of the two-dimensional (2D) images. Inspired by Kam’s method, we introduce a rotationally invariant metric between two molecular structures, which does not require 3D alignment. Further, we introduce a metric between a stack of projection images and a molecular structure, which is invariant to rotations and reflections and does not require performing 3D reconstruction. Additionally, the latter metric does not assume a uniform distribution of viewing angles. We demonstrate the uses of the new metrics on synthetic and experimental datasets, highlighting their ability to measure structural similarity.

Single-particle cryo-electron microscopy (cryo-EM) is a powerful imaging modality capable of visualizing proteins and macromolecular complexes at near-atomic resolution. The low electron-doses used to prevent radiation damage to the biological samples, however, result in images where the power of the noise is 100 times greater than the power of the signal. To overcome these low signal-to-noise ratios (SNRs), hundreds of thousands of particle projections are averaged to determine the three-dimensional structure of the molecule of interest. The sampling requirements of high-resolution imaging impose limitations on the pixel sizes that can be used for acquisition, limiting the size of the field of view and requiring data collection sessions of several days to accumulate sufficient numbers of particles. Meanwhile, recent image super-resolution (SR) techniques based on neural networks have shown state-of-the-art performance on natural images. Building on these advances, here, we present a multiple-image SR algorithm based on deep internal learning designed specifically to work under low-SNR conditions. Our approach leverages the internal image statistics of cryo-EM movies and does not require training on ground-truth data. When applied to single-particle datasets of apoferritin and T20S proteasome, we show that the resolution of the 3D structure obtained from SR micrographs can surpass the limits imposed by the imaging system. Our results indicate that the combination of low magnification imaging with in silico image SR has the potential to accelerate cryo-EM data collection by virtue of including more particles in each exposure and doing so without sacrificing resolution.

Cryo-electron microscopy (cryo-EM) is an imaging technique that allows the visualization of proteins and macromolecular complexes at near-atomic resolution. The low electron doses used to prevent radiation damage to the biological samples result in images where the power of noise is 100 times stronger than that of the signal. Accurate identification of proteins from these low signal-to-noise ratio (SNR) images is a critical task, as the detected positions serve as inputs for the downstream 3D structure determination process. Current methods either fail to identify all true positives or result in many false positives, especially when analyzing images from smaller-sized proteins that exhibit extremely low contrast, or require manual labeling that can take days to complete. Acknowledging the fact that accurate protein identification is dependent upon the visual interpretability of micrographs, we propose a framework that can perform denoising and detection in a joint manner and enable particle localization under extremely low SNR conditions using self-supervised denoising and particle identification from sparsely annotated data. We validate our approach on three challenging single-particle cryo-EM datasets and projection images from one cryo-electron tomography dataset with extremely low SNR, showing that it outperforms existing state-of-the-art methods used for cryo-EM image analysis by a significant margin. We also evaluate the performance of our algorithm under decreasing SNR conditions and show that our method is more robust to noise than competing methods.

In this article, we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance between the density maps after a rigid transformation. The induced loss function enjoys a more benign landscape than its Euclidean counterpart and Bayesian optimization is employed for computation. Numerical experiments show improved accuracy and efficiency over existing algorithms on the alignment of real protein molecules. In the context of aligning heterogeneous pairs, we illustrate a potential need for new distance functions.

In this work, we present a pair of tools to improve the fiducial tracking and reconstruction quality of cryo-scanning transmission electron tomography (STET) datasets. We then demonstrate the effectiveness of these two tools on experimental cryo-STET data. The first tool, GoldDigger, improves the tracking of fiducials in cryo-STET by accommodating the changed appearance of highly defocussed fiducial markers. Since defocus effects are much stronger in scanning transmission electron microscopy than in conventional transmission electron microscopy, existing alignment tools do not perform well without manual intervention. The second tool, Checkers, combines image inpainting and unsupervised deep learning for denoising tomograms. Existing tools for denoising cryo-tomography often rely on paired noisy image frames, which are unavailable in cryo-STET datasets, necessitating a new approach. Finally, we make the two software tools freely available for the cryo-STET community.

Different tasks in the computational pipeline of single-particle cryo-electron microscopy (cryo-EM) require enhancing the quality of the highly noisy raw images. To this end, we develop an efficient algorithm for signal enhancement of cryo-EM images. The enhanced images can be used for a variety of downstream tasks, such as two-dimensional classification, removing uninformative images, constructing ab initio models, generating templates for particle picking, providing a quick assessment of the data set, dimensionality reduction, and symmetry detection. The algorithm includes built-in quality measures to assess its performance and alleviate the risk of model bias. We demonstrate the effectiveness of the proposed algorithm on several experimental data sets. In particular, we show that the quality of the resulting images is high enough to produce ab initio models of $ \sim 10 $ Å resolution. The algorithm is accompanied by a publicly available, documented, and easy-to-use code.

A common task in cryo-electron microscopy data processing is to compare three-dimensional density maps of macromolecules. In this paper, we propose an algorithm for aligning three-dimensional density maps, which exploits common lines between projection images of the maps. The algorithm is fully automatic and handles rotations, reflections (handedness), and translations between the maps. In addition, the algorithm is applicable to any type of molecular symmetry without requiring any information regarding the symmetry of the maps. We evaluate our alignment algorithm on publicly available density maps, demonstrating its accuracy and efficiency. The algorithm is available at https://github.com/ShkolniskyLab/emalign.

An emergent volume electron microscopy technique called cryogenic serial plasma focused ion beam milling scanning electron microscopy (pFIB/SEM) can decipher complex biological structures by building a three-dimensional picture of biological samples at mesoscale resolution. This is achieved by collecting consecutive SEM images after successive rounds of FIB milling that expose a new surface after each milling step. Due to instrumental limitations, some image processing is necessary before 3D visualization and analysis of the data is possible. SEM images are affected by noise, drift, and charging effects, that can make precise 3D reconstruction of biological features difficult. This article presents Okapi-EM, an open-source napari plugin developed to process and analyze cryogenic serial pFIB/SEM images. Okapi-EM enables automated image registration of slices, evaluation of image quality metrics specific to pFIB-SEM imaging, and mitigation of charging artifacts. Implementation of Okapi-EM within the napari framework ensures that the tools are both user- and developer-friendly, through provision of a graphical user interface and access to Python programming.

Electron cryo-tomography is an imaging technique for probing 3D structures with at the nanometer scale. This technique has been used extensively in the biomedical field to study the complex structures of proteins and other macromolecules. With the advancement in technology, microscopes are currently capable of producing images amounting to terabytes of data per day, posing great challenges for scientists as the speed of processing of the images cannot keep up with the ever-higher throughput of the microscopes. Therefore, automation is an essential and natural pathway on which image processing—from individual micrographs to full tomograms—is developing. In this paper, we present Ot2Rec, an open-source pipelining tool which aims to enable scientists to build their own processing workflows in a flexible and automatic manner. The basic building blocks of Ot2Rec are plugins which follow a unified application programming interface structure, making it simple for scientists to contribute to Ot2Rec by adding features which are not already available. In this paper, we also present three case studies of image processing using Ot2Rec, through which we demonstrate the speedup of using a semi-automatic workflow over a manual one, the possibility of writing and using custom (prototype) plugins, and the flexibility of Ot2Rec which enables the mix-and-match of plugins. We also demonstrate, in the Supplementary Material, a built-in reporting feature in Ot2Rec which aggregates the metadata from all process being run, and output them in the Jupyter Notebook and/or HTML formats for quick review of image processing quality. Ot2Rec can be found at https://github.com/rosalindfranklininstitute/ot2rec.

Image-processing pipelines require the design of complex workflows combining many different steps that bring the raw acquired data to a final result with biological meaning. In the image-processing domain of cryo-electron microscopy single-particle analysis (cryo-EM SPA), hundreds of steps must be performed to obtain the three-dimensional structure of a biological macromolecule by integrating data spread over thousands of micrographs containing millions of copies of allegedly the same macromolecule. The execution of such complicated workflows demands a specific tool to keep track of all these steps performed. Additionally, due to the extremely low signal-to-noise ratio (SNR), the estimation of any image parameter is heavily affected by noise resulting in a significant fraction of incorrect estimates. Although low SNR and processing millions of images by hundreds of sequential steps requiring substantial computational resources are specific to cryo-EM, these characteristics may be shared by other biological imaging domains. Here, we present Scipion, a Python generic open-source workflow engine specifically adapted for image processing. Its main characteristics are: (a) interoperability, (b) smart object model, (c) gluing operations, (d) comparison operations, (e) wide set of domain-specific operations, (f) execution in streaming, (g) smooth integration in high-performance computing environments, (h) execution with and without graphical capabilities, (i) flexible visualization, (j) user authentication and private access to private data, (k) scripting capabilities, (l) high performance, (m) traceability, (n) reproducibility, (o) self-reporting, (p) reusability, (q) extensibility, (r) software updates, and (s) non-restrictive software licensing.