  Single particle cryo-electron microscopy is a vital tool for 3D
characterization of protein structures. A typical workflow involves acquiring
projection images of a collection of randomly oriented particles, picking and
classifying individual particle projections by orientation, and finally using
the individual particle projections to reconstruct a 3D map of the electron
density profile. The reconstruction is challenging because of the low
signal-to-noise ratio of the data, the unknown orientation of the particles,
and the sparsity of data especially when dealing with flexible proteins where
there may not be sufficient data corresponding to each class to obtain an
accurate reconstruction using standard algorithms. In this paper we present a
model-based image reconstruction technique that uses a regularized cost
function to reconstruct the 3D density map by assuming known orientations for
the particles. Our method casts the reconstruction as minimizing a cost
function involving a novel forward model term that accounts for the contrast
transfer function of the microscope, the orientation of the particles and the
center of rotation offsets. We combine the forward model term with a
regularizer that enforces desirable properties in the volume to be
reconstructed. Using simulated data, we demonstrate how our method can
significantly improve upon the typically used approach.
