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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., Comment: 27 pages, 9 figures

Thanks to automated cryo-EM and GPU-accelerated processing, single-particle cryo-EM has become a rapid structure determination method that permits capture of dynamical structures of molecules in solution, which has been recently demonstrated by the determination of COVID-19 spike protein in March, shortly after its breakout in late January 2020. This rapidity is critical for vaccine development in response to emerging pandemic. This explains why a 2D classification approach based on multi-reference alignment (MRA) is not as popular as the Bayesian-based approach despite that the former has advantage in differentiating structural variations under low signal-to-noise ratio. This is perhaps because that MRA is a time-consuming process and a modular GPU-acceleration library for MRA is lacking. Here, we introduce a library called Cryo-RALib that expands the functionality of CUDA library used by GPU ISAC. It contains a GPU-accelerated MRA routine for accelerating MRA-based classification algorithms. In addition, we connect the cryo-EM image analysis with the python data science stack so as to make it easier for users to perform data analysis and visualization. Benchmarking on the TaiWan Computing Cloud (TWCC) container shows that our implementation can accelerate the computation by one order of magnitude. The library is available at https://github.com/phonchi/Cryo-RAlib.

Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an eigenvalue problem for the sample covariance matrix. We propose herein a two-stage dimension reduction (2SDR) method for image reconstruction from high-dimensional noisy image data. The first stage treats the image as a matrix, which is a tensor of order 2, and uses multilinear principal component analysis (MPCA) for matrix rank reduction and image denoising. The second stage vectorizes the reduced-rank matrix and achieves further dimension and noise reduction. Simulation studies demonstrate excellent performance of 2SDR, for which we also develop an asymptotic theory that establishes consistency of its rank selection. Applications to cryo-EM (cryogenic electronic microscopy), which has revolutionized structural biology, organic and medical chemistry, cellular and molecular physiology in the past decade, are also provided and illustrated with benchmark cryo-EM datasets. Connections to other contemporaneous developments in image reconstruction and high-dimensional statistical inference are also discussed., Comment: 29 pages, 8 figures and 3 tables