A graph theory method for determination of cryo-EM image focuses

Accurate determination of micrograph focuses is essential for averaging multiple images to reach high-resolution 3-D reconstructions in electron cryo-microscopy (cryo-EM). Current methods use iterative fitting of focus-dependent simulated power spectra to the power spectra of experimental images, with the fitting performed independently for different images. Here we have developed a novel graph theory based method in which the rotational average focus and individual angular sector focuses of all images are determined simultaneously in closed form using the least square solution of overdetermined linear equations. The new method was shown to be fast, accurate, and robust in tests with large datasets of experimental low dose cryo-EM images. Its integration with three classic power spectra fitting methods also allows cross validation of the results by these vastly different methods. The new integrated focus determination method will improve reliability of automated focus determination for large-scale data processing that is increasingly common in the cryo-EM field.