Single-particle cryo electron microscopy experiments provide a single, approximately tomographic, image of each of a thousand to a hundred thousand instances of a particle of interest. Reconstruction of the electron scattering intensity of the particle in 3-D can be performed by many software systems. Some systems can characterize the heterogeneity of the particles. Particles with a rotational point group symmetry are relatively common in biology, e.g., 31.0, 7.5, 0.5, 0.3, and 0.2 percent of the Protein Data Bank entries have cyclic, dihedral, icosahedral, tetrahedral, or octahedral symmetry, respectively. A computational system that simultaneously estimates the electron scattering intensity and characterizes the heterogeneity of the intensity by estimating both the first-and second-order statistics of the intensity is described where the statistics, rather than the reconstruction, are constrained to have a symmetry.

The work represents a collaboration with Yunye Gong (current Ph.D. student in ECE at Cornell), Nan Xu, Qiu Wang, and Yili Zheng (former Ph.D. students), and John E. Johnson (The Scripps Research Institute).