A Bayesian approach for suppression of limited angular sampling artifacts in single particle 3D reconstruction

Advances in image processing for single-particle analysis by electron cryomicroscopy and challenges ahead

Electron cryomicroscopy (cryoEM) is essential for the study and functional understanding of non-crystalline macromolecules such as proteins. These molecules cannot be imaged using X-ray crystallography or other popular methods. CryoEM has been successfully used to visualize macromolecular complexes such as ribosomes, viruses, and ion channels. Determination of structural models of these at various conformational states leads to insight on how these molecules function. Recent advances in imaging technology have given cryoEM a scientific rebirth. As a result of these technological advances image processing and analysis have yielded molecular structures at atomic resolution. Nevertheless there continue to be challenges in image processing, and in this article we will touch on the most essential in order to derive an accurate three-dimensional model from noisy projection images. Traditional approaches, such as k-means clustering for class averaging, will be provided as background. We will then highlight new approaches for each image processing subproblem, including a 3D reconstruction method for asymmetric molecules using just two projection images and deep learning algorithms for automated particle picking.

Likelihood-based structural analysis of electron microscopy images

Likelihood-based analysis of single-particle electron microscopy images has contributed much to the recent improvements in resolution. By treating particle orientations and classes probabilistically, uncertainties in the reconstruction process are explicitly accounted for, and the risk of bias towards the initial model is diminished. As a result, the quality and reliability of the reconstructions have greatly improved at manageable computational cost. Likelihood-based analysis of electron microscopy images also offers a route to direct coordinate refinement for dynamic systems, as an alternative to 3D density reconstruction. Here, we review recent developments in the algorithms used for reconstructions of high-resolution maps, and in the integrative framework of combining likelihood methods with simulations to address conformational variability in cryo-electron microscopy.

A Survey of the Use of Iterative Reconstruction Algorithms in Electron Microscopy

One of the key steps in Electron Microscopy is the tomographic reconstruction of a three-dimensional (3D) map of the specimen being studied from a set of two-dimensional (2D) projections acquired at the microscope. This tomographic reconstruction may be performed with different reconstruction algorithms that can be grouped into several large families: direct Fourier inversion methods, back-projection methods, Radon methods, or iterative algorithms. In this review, we focus on the latter family of algorithms, explaining the mathematical rationale behind the different algorithms in this family as they have been introduced in the field of Electron Microscopy. We cover their use in Single Particle Analysis (SPA) as well as in Electron Tomography (ET).

Adaptive multiresolution method for MAP reconstruction in electron tomography

3D image reconstruction with electron tomography holds problems due to the severely limited range of projection angles and low signal to noise ratio of the acquired projection images. The maximum a posteriori (MAP) reconstruction methods have been successful in compensating for the missing information and suppressing noise with their intrinsic regularization techniques. There are two major problems in MAP reconstruction methods: (1) selection of the regularization parameter that controls the balance between the data fidelity and the prior information, and (2) long computation time. One aim of this study is to provide an adaptive solution to the regularization parameter selection problem without having additional knowledge about the imaging environment and the sample. The other aim is to realize the reconstruction using sequences of resolution levels to shorten the computation time. The reconstructions were analyzed in terms of accuracy and computational efficiency using a simulated biological phantom and publically available experimental datasets of electron tomography. The numerical and visual evaluations of the experiments show that the adaptive multiresolution method can provide more accurate results than the weighted back projection (WBP), simultaneous iterative reconstruction technique (SIRT), and sequential MAP expectation maximization (sMAPEM) method. The method is superior to sMAPEM also in terms of computation time and usability since it can reconstruct 3D images significantly faster without requiring any parameter to be set by the user.