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Tuesday, September 3, 2019

**Abstract:** We introduce a novel intrinsic classification algorithm--multi-frequency class averaging (MFCA)--for clustering noisy projection images obtained from three-dimensional cryo-electron microscopy (cryo-EM) by the similarity among their viewing directions. This new algorithm leverages multiple irreducible representations of the unitary group to introduce additional redundancy into the representation of the transport data, extending and outperforming the previous class averaging algorithm that uses only a single representation. We will discuss the formal algebraic model and representation theoretic patterns of the proposed MFCA algorithm. We conceptually establish the consistency and stability of MFCA by inspecting the spectral properties of a generalized localized parallel transport operator on the two-dimensional unit sphere through the lens of Wigner D-matrices. We will also show how this algorithm can be applied to directly denoise the real data.