  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.
