Fast and Robust Algorithms in Cryo-Electron Microscopy Imaging

Cryo-electron microscopy (cryo-EM) has revolutionized the way scientists uncover the 3D structure of proteins, making critical contributions to our understanding of viruses, cancer, and neurodegenerative diseases. However, despite its transformative potential, cryo-EM is limited by the immense computational cost required to process the large, noisy, and unstructured image data it generates. This project aims to overcome these barriers by developing robust, efficient, and theoretically guaranteed algorithms for reconstructing 3D molecular structures from raw cryo-EM data. These algorithms will allow researchers to extract higher-resolution structures more quickly and reliably, accelerating scientific discoveries in biomedicine and supporting translational science in areas like drug development. Graduate student training will also be included in this project. Technically, the project addresses two critical stages of the cryo-EM pipeline: image alignment and molecular orientation estimation. For image alignment, the project will develop new shift-robust and deformation-tolerant metrics to improve classification and registration of raw 2D images. For orientation estimation, the project will develop a novel, decentralized message-passing algorithm to synchronize noisy and partially corrupted pairwise measurements of euclidean motions of 2D images and 3D molecules. By leveraging tools from harmonic analysis, optimal transport, and Riemannian optimization, the proposed methods will significantly improve the speed, accuracy, and transparency of current reconstruction techniques. These innovations will be implemented as open-source software, broadly benefiting applications in biomedical imaging, computer vision, and robotics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.