Cryo-forum: A framework for orientation recovery with uncertainty measure with the application in cryo-EM image analysis

In single-particle cryo-electron microscopy (cryo-EM), the efficient determination of orientation parameters for 2D projection images poses a significant challenge yet is crucial for reconstructing 3D structures. This task is complicated by the high noise levels present in the cryo-EM datasets, which often include outliers, necessitating several time-consuming 2D clean-up processes. Recently, solutions based on deep learning have emerged, offering a more streamlined approach to the traditionally laborious task of orientation estimation. These solutions often employ amortized inference, eliminating the need to estimate parameters individually for each image. However, these methods frequently overlook the presence of outliers and may not adequately concentrate on the components used within the network. This paper introduces a novel approach that uses a 10-dimensional feature vector to represent the orientation and applies a Quadratically-Constrained Quadratic Program to derive the predicted orientation as a unit quaternion, supplemented by an uncertainty metric. Furthermore, we propose a unique loss function that considers the pairwise distances between orientations, thereby enhancing the accuracy of our method. Finally, we also comprehensively evaluate the design choices involved in constructing the encoder network, a topic that has not received sufficient attention in the literature. Our numerical analysis demonstrates that our methodology effectively recovers orientations from 2D cryo-EM images in an end-to-end manner. Importantly, the inclusion of uncertainty quantification allows for direct clean-up of the dataset at the 3D level. Lastly, we package our proposed methods into a user-friendly software suite named cryo-forum, designed for easy accessibility by the developers.

2SDR: Applying Kronecker Envelope PCA to denoise Cryo-EM Images

Principal component analysis (PCA) is arguably the most widely used dimension reduction method for vector type data. When applied to image data, PCA demands the images to be portrayed as vectors. The resulting computation is heavy because it will solve an eigenvalue problem of a huge covariance matrix due to the vectorization step. To mitigate the computation burden, multilinear PCA (MPCA) that generates each basis vector using a column vector and a row vector with a Kronecker product was introduced, for which the success was demonstrated on face image sets. However, when we apply MPCA on the cryo-electron microscopy (cryo-EM) particle images, the results are not satisfactory when compared with PCA. On the other hand, to compare the reduced spaces as well as the number of parameters of MPCA and PCA, Kronecker Envelope PCA (KEPCA) was proposed to provide a PCA-like basis from MPCA. Here, we apply KEPCA to denoise cryo-EM images through a two-stage dimension reduction (2SDR) algorithm. 2SDR first applies MPCA to extract the projection scores and then applies PCA on these scores to further reduce the dimension. 2SDR has two benefits that it inherits the computation advantage of MPCA and its projection scores are uncorrelated as those of PCA. Testing with three cryo-EM benchmark experimental datasets shows that 2SDR performs better than MPCA and PCA alone in terms of the computation efficiency and denoising quality. Remarkably, the denoised particles boxed out from the 2SDR-denoised micrographs allow subsequent structural analysis to reach a high-quality 3D density map. This demonstrates that the high resolution information can be well preserved through this 2SDR denoising strategy.