Search

One of the challenges in single particle reconstruction in cryo-electron microscopy is to find a three-dimensional model of a molecule using its two-dimensional noisy projection-images. In this paper, we propose a robust "angular reconstitution" algorithm for molecules with $n$-fold cyclic symmetry, that estimates the orientation parameters of the projections-images. Our suggested method utilizes self common lines which induce identical lines within the Fourier transform of each projection-image. We show that the location of self common lines admits quite a few favorable geometrical constraints, thus allowing to detect them even in a noisy setting. In addition, for molecules with higher order rotational symmetry, our proposed method exploits the fact that there exist numerous common lines between any two Fourier transformed projection-images of such molecules, thus allowing to determine their relative orientation even under high levels of noise. The efficacy of our proposed method is demonstrated using numerical experiments conducted on simulated and experimental data.

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.