  Cryo-electron microscopy (cryo-EM) is capable of producing reconstructed 3D
images of biomolecules at near-atomic resolution. As such, it represents one of
the most promising imaging techniques in structural biology. However, raw
cryo-EM images are only highly corrupted - noisy and band-pass filtered - 2D
projections of the target 3D biomolecules. Reconstructing the 3D molecular
shape starts with the removal of image outliers, the estimation of the
orientation of the biomolecule that has produced the given 2D image, and the
estimation of camera parameters to correct for intensity defects. Current
techniques performing these tasks are often computationally expensive, while
the dataset sizes keep growing. There is a need for next-generation algorithms
that preserve accuracy while improving speed and scalability. In this paper, we
combine variational autoencoders (VAEs) and generative adversarial networks
(GANs) to learn a low-dimensional latent representation of cryo-EM images. We
perform an exploratory analysis of the obtained latent space, that is shown to
have a structure of "orbits", in the sense of Lie group theory, consistent with
the acquisition procedure of cryo-EM images. This analysis leads us to design
an estimation method for orientation and camera parameters of single-particle
cryo-EM images, together with an outliers detection procedure. As such, it
opens the door to geometric approaches for unsupervised estimations of
orientations and camera parameters, making possible fast cryo-EM biomolecule
reconstruction.
