  Single-particle cryo-electron microscopy (cryo-EM) is a leading technology to
resolve the structure of molecules. Early in the process, the user detects
potential particle images in the raw data. Typically, there are many false
detections as a result of high levels of noise and contamination. Currently,
removing the false detections requires human intervention to sort the hundred
thousands of images. We propose a statistically-established unsupervised
algorithm to remove non-particle images. We model the particle images as a
union of low-dimensional subspaces, assuming non-particle images are
arbitrarily scattered in the high-dimensional space. The algorithm is based on
an extension of the probabilistic PCA framework to robustly learn a non-linear
model of union of subspaces. This provides a flexible model for cryo-EM data,
and allows to automatically remove images that correspond to pure noise and
contamination. Numerical experiments corroborate the effectiveness of the
sorting algorithm.
