School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China.
College of Computer Science and Engineering, Northwest Normal University, Lanzhou 730070, China.
Curr Issues Mol Biol. 2021 Oct 18;43(3):1652-1668. doi: 10.3390/cimb43030117.
Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-EM is an important procedure for producing high-quality initial 3D structures, where image alignment is a fundamental step. In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters of rotation angles and translational shifts between the two projection images, which can obtain subpixel and subangle accuracy. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed image alignment algorithm and a spectral clustering algorithm are used to compute class averages for single-particle 3D reconstruction. The proposed image alignment algorithm is firstly tested on a Lena image and two cryo-EM datasets. Results show that the proposed image alignment algorithm can estimate the alignment parameters accurately and efficiently. The proposed method is also used to reconstruct preliminary 3D structures from a simulated cryo-EM dataset and a real cryo-EM dataset and to compare them with RELION. Experimental results show that the proposed method can obtain more high-quality class averages than RELION and can obtain higher reconstruction resolution than RELION even without iteration.
三维（3D）重建在单颗粒冷冻电子显微镜（cryo-EM）中是一种从未知随机方向拍摄的二维（2D）噪声投影图像中恢复蛋白质或其他生物大分子 3D 结构的重要技术。在单颗粒 cryo-EM 中，分类平均是产生高质量初始 3D 结构的重要步骤，其中图像对齐是基本步骤。在本文中，提出了一种使用图像频域中的 2D 插值的高效图像对齐算法，以提高旋转角度和两个投影图像之间平移偏移的对齐参数估计精度，该算法可以实现亚像素和亚角度精度。该算法首先使用两个投影图像的傅里叶变换计算离散互相关矩阵，然后在互相关矩阵中的最大值周围进行 2D 插值。根据插值后的互相关矩阵中最大值的位置，直接确定对齐参数。此外，还使用所提出的图像对齐算法和谱聚类算法计算单颗粒 3D 重建的分类平均值。所提出的图像对齐算法首先在 Lena 图像和两个 cryo-EM 数据集上进行测试。结果表明，所提出的图像对齐算法可以准确高效地估计对齐参数。还将所提出的方法用于从模拟 cryo-EM 数据集和真实 cryo-EM 数据集重建初步 3D 结构，并与 RELION 进行比较。实验结果表明，与 RELION 相比，所提出的方法可以获得更高质量的分类平均值，并且即使没有迭代，也可以获得比 RELION 更高的重建分辨率。
