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Determining the three-dimensional (3D) structure of proteins and protein complexes at atomic resolution is a fundamental task in structural biology. Over the last decade, remarkable progress has been made using “single particle” cryo-electron microscopy (cryo-EM) for this purpose. In cryo-EM, hundreds of thousands of two-dimensional (2D) images are obtained of individual copies of the same particle, each held in a thin sheet of ice at some unknown orientation. Each image corresponds to the noisy projection of the particleu0027s electron-scattering density. The reconstruction of a high-resolution image from this data is typically formulated as a nonlinear, nonconvex optimization problem for unknowns which encode the angular pose and lateral offset of each particle. Since there are hundreds of thousands of such parameters, this leads to a very CPU-intensive task---limiting both the number of particle images which can be processed and the number of independent reconstructions which can be carried out for the pur...

Rapid Solution of the Cryo-EM Reconstruction Problem by Frequency Marching