  A main task in cryo-electron microscopy single particle reconstruction is to
find a three-dimensional model of a molecule given a set of its randomly
oriented and positioned noisy projection-images. In this work, we propose an
algorithm for ab-initio reconstruction for molecules with tetrahedral or
octahedral symmetry. The algorithm exploits the multiple common lines between
each pair of projection-images as well as self common lines within each image.
It is robust to noise in the input images as it integrates the information from
all images at once. The applicability of the proposed algorithm is demonstrated
using experimental cryo-electron microscopy data.
