Representation theoretic patterns in multi-frequency class averaging for three-dimensional cryo-electron microscopy

Abstract We develop in this paper a novel intrinsic classification algorithm—multi-frequency class averaging (MFCA)—for classifying noisy projection images obtained from three-dimensional cryo-electron microscopy by the similarity among their viewing directions. This new algorithm leverages multiple irreducible representations of unitary group to introduce additional redundancy into representation optimal in-plane rotational alignment, extending and outperforming existing that uses only single representation. The formal algebraic model theoretic patterns proposed MFCA extend framework Hadani Singer arbitrary group. conceptually establish consistency stability inspecting spectral properties generalized local parallel transport operator through lens Wigner $D$-matrices. demonstrate efficacy with numerical experiments.