  We target the problem of estimating the center of mass of noisy 2-D images.
We assume that the noise dominates the image, and thus many standard approaches
are vulnerable to estimation errors. Our approach uses a surrogate function to
the geometric median, which is a robust estimator of the center of mass. We
mathematically analyze cases in which the geometric median fails to provide a
reasonable estimate of the center of mass, and prove that our surrogate
function leads to a successful estimate.
  One particular application for our method is to improve 3-D reconstruction in
single-particle cryo-electron microscopy (cryo-EM). We show how to apply our
approach for a better translational alignment of macromolecules picked from
experimental data. In this way, we facilitate the succeeding steps of
reconstruction and streamline the entire cryo-EM pipeline, saving valuable
computational time and supporting resolution enhancement.
