Determining the three-dimensional 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. The reconstruction of a high-resolution image from cryo-EM data is typically formulated as a nonlinear, non-convex optimization problem for hundreds of thousands of unknown 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 purpose of statistical validation. Here, we propose a deterministic method for high-resolution reconstruction given a very low resolution initial guess, that requires a predictable and relatively modest amount of computational effort.