Electron cryo-microscopy (cryoEM) is now a powerful tool in determining atomic structures of biological macromolecules under nearly natural conditions. The major task of single-particle cryoEM is to estimate a set of parameters for each input particle image to reconstruct the three-dimensional structure of the macromolecules. As future large-scale applications require increasingly higher resolution and automation, robust high-dimensional parameter estimation algorithms need to be developed in the presence of various image qualities. In this paper, we introduced a particle-filter algorithm for cryoEM, which was a sequential Monte Carlo method for robust and fast high-dimensional parameter estimation. The cryoEM parameter estimation problem was described by a probability density function of the estimated parameters. The particle filter uses a set of random and weighted support points to represent such a probability density function. The statistical properties of the support points not only enhance the parameter estimation with self-adaptive accuracy but also provide the belief of estimated parameters, which is essential for the reconstruction phase. The implementation of these features showed strong tolerance to bad particles and enabled robust defocus refinement, demonstrated by the remarkable resolution improvement at the atomic level.
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