Subspace Method of Moments for

Cryo-electron microscopy (cryo-EM) is a widely used technique for recovering the three-dimensional (3-D) structure of biological molecules from a large number of experimentally generated noisy 2-D tomographic projection images of the 3-D structure, taken from unknown viewing angles. Through computationally intensive algorithms, these observed images are processed to reconstruct the 3-D structures. Many popular computational methods rely on estimating the unknown angles as part of the reconstruction process, which becomes particularly challenging at low signal-to-noise ratios. The method of moments offers an alternative approach that circumvents the estimation of viewing orientations of individual projection images by instead estimating the underlying distribution of the viewing angles, and is robust to noise given sufficiently many images. However, the method of moments typically entails computing higher-order moments of the projection images, incurring significant computational and memory costs. To mitigate this, we propose a new approach called the subspace method of moments (SubspaceMoM), which compresses the first three moments using data-driven low-rank tensor techniques as well as expansion into a suitable function basis. The compressed moments can be efficiently computed from the set of projection images using numerical quadrature and can be employed to jointly reconstruct the 3-D structure and the distribution of viewing orientations. We illustrate the practical applicability of SubspaceMoM through numerical experiments using up to the third-order moment on synthetic datasets with a simplified cryo-EM image formation model, which significantly improves the reconstruction resolution compared to previous MoM approaches.