  The field of cryo-electron microscopy has made astounding advancements in the
past few years, mainly due to advancements in electron detectors' technology.
Yet, one of the key open challenges of the field remains the processing of
heterogeneous data sets, produced from samples containing particles at several
different conformational states. For such data sets, the algorithms must
include some classification procedure to identify homogeneous groups within the
data, so that the images in each group correspond to the same underlying
structure. The fundamental importance of the heterogeneity problem in
cryo-electron microscopy has drawn many research efforts, and resulted in
significant progress in classification algorithms for heterogeneous data sets.
While these algorithms are extremely useful and effective in practice, they
lack rigorous mathematical analysis and performance guarantees.
  In this paper, we attempt to make the first steps towards rigorous
mathematical analysis of the heterogeneity problem in cryo-electron microscopy.
To that end, we present an algorithm for processing heterogeneous data sets,
and prove accuracy and stability bounds for it. We also suggest an extension of
this algorithm that combines the classification and reconstruction steps. We
demonstrate it on simulated data, and compare its performance to the
state-of-the-art algorithm in RELION.
