Determining fluctuation in bio-nanomachines from electron microscopy images

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 is heterogeneous, it is natural to describe the object as stochastic with unknown statistics and seek to estimate the statistics from the image data. The result is not a unique reconstruction but rather a statistical description of an ensemble of reconstructions where the mean of the ensemble is a natural choice if a unique reconstruction is desired. This paper describes maximum likelihood methods for estimating the statistics via an expectation-maximization algorithm and multiple algorithmic optimizations to speed up the calculations.