  A major challenge in single-particle cryo-electron microscopy (cryo-EM) is
that the orientations adopted by the 3D particles prior to imaging are unknown;
yet, this knowledge is essential for high-resolution reconstruction. We present
a method to recover these orientations directly from the acquired set of 2D
projections. Our approach consists of two steps: (i) the estimation of
distances between pairs of projections, and (ii) the recovery of the
orientation of each projection from these distances. In step (i), pairwise
distances are estimated by a Siamese neural network trained on synthetic
cryo-EM projections from resolved bio-structures. In step (ii), orientations
are recovered by minimizing the difference between the distances estimated from
the projections and the distances induced by the recovered orientations. We
evaluated the method on synthetic cryo-EM datasets. Current results demonstrate
that orientations can be accurately recovered from projections that are shifted
and corrupted with a high level of noise. The accuracy of the recovery depends
on the accuracy of the distance estimator. While not yet deployed in a real
experimental setup, the proposed method offers a novel learning-based take on
orientation recovery in SPA. Our code is available at
https://github.com/JelenaBanjac/protein-reconstruction
