  Cryogenic electron microscopy (cryo-EM) provides images from different copies
of the same biomolecule in arbitrary orientations. Here, we present an
end-to-end unsupervised approach that learns individual particle orientations
from cryo-EM data while reconstructing the average 3D map of the biomolecule,
starting from a random initialization. The approach relies on an auto-encoder
architecture where the latent space is explicitly interpreted as orientations
used by the decoder to form an image according to the linear projection model.
We evaluate our method on simulated data and show that it is able to
reconstruct 3D particle maps from noisy- and CTF-corrupted 2D projection images
of unknown particle orientations.
