A Graph Partitioning Approach to Simultaneous Angular Reconstitution

One of the primary challenges in single particle reconstruction with cryo-electron microscopy is to find a three-dimensional model of a molecule using its noisy two-dimensional projection-images. As the imaging orientations of the projection-images are unknown, we suggest a common-lines-based method to simultaneously estimate the imaging orientations of all images that is independent of the distribution of the orientations. Since the relative orientation of each pair of images may only be estimated up to a two-way handedness ambiguity, we suggest an efficient procedure to consistently assign the same handedness to all relative orientations. This is achieved by casting the handedness assignment problem as a graph-partitioning problem. Once a consistent handedness of all relative orientations is determined, the orientations corresponding to all projection-images are determined simultaneously, thus rendering the method robust to noise. Our proposed method has also the advantage of allowing one to incorporate confidence information regarding the trustworthiness of each relative orientation in a natural manner. We demonstrate the efficacy of our approach using simulated clean and noisy data.