Orientation Determination of Cryo-EM Projection Images Using Reliable Common Lines and Spherical Embeddings

Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a critical technique for recovering and studying the fine 3D structure of proteins and other biological macromolecules, where the primary issue is to determine the orientations of projection images with high levels of noise. This paper proposes a method to determine the orientations of cryo-EM projection images using reliable common lines and spherical embeddings. First, the reliability of common lines between projection images is evaluated using a weighted voting algorithm based on an iterative improvement technique and binarized weighting. Then, the reliable common lines are used to calculate the normal vectors and local X-axis vectors of projection images after two spherical embeddings. Finally, the orientations of projection images are determined by aligning the results of the two spherical embeddings using an orthogonal constraint. Experimental results on both synthetic and real cryo-EM projection image datasets demonstrate that the proposed method can achieve higher accuracy in estimating the orientations of projection images and higher resolution in reconstructing preliminary 3D structures than some common line-based methods, indicating that the proposed method is effective in single-particle cryo-EM 3D reconstruction.