Reconstruction for stochastic 3-D signals with symmetric statistics in noise: Electron microscopy of virus particles

Cryo electron microscopy leads to 3-D image reconstruction problems. The data is one projection of each of many different instances of the object. When the object has symmetry and is also heterogeneous, it is natural to describe the object as stochastic with symmetrical statistics. This paper describes methods for incorporating the symmetry into expectation-maximization algorithms for the maximum likelihood solution of the reconstruction problem.