End-to-end orientation estimation from 2D cryo-EM images.

Cryo-electron microscopy (cryo-EM) is a Nobel Prize-winning technique for determining high-resolution 3D structures of biological macromolecules. A 3D structure is reconstructed from hundreds of thousands of noisy 2D projection images. However, existing 3D reconstruction methods are still time-consuming, and one of the major computational bottlenecks is recovering the unknown orientation of the particle in each 2D image. The dominant methods typically exploit an expensive global search on each image to estimate the missing orientations. Here, a novel end-to-end supervised learning method is introduced to directly recover the missing orientations from 2D cryo-EM images. A neural network is used to approximate the mapping from images to orientations. A robust loss function is proposed for optimizing the parameters of the network, which can handle both asymmetric and symmetric 3D structures. Experiments on synthetic data sets with various symmetry types confirm that the neural network is capable of recovering orientations from 2D cryo-EM images, and the results on a real cryo-EM data set further demonstrate its potential under more challenging imaging conditions.