Bayesian perspective for orientation determination in cryo-EM with application to structural heterogeneity analysis

Xu, S.; Balanov, A.; Singer, A.; Bendory, T.

doi:10.1107/S2059798326001415

Acta Crystallographica Section D
Acta Crystallographica
Section D STRUCTURAL BIOLOGY

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Figure 3
Impact of the sampling-grid size of $[{\sf{SO}}(3)]$ (L) and the signal-to-noise ratio (SNR) on rotation-estimation accuracy. This figure shows the accuracy of rotation estimation under varying sampling-grid sizes L of the rotation group $[{\sf{SO}}(3)]$ and different SNR levels of the observed data y in the model (3). Simulations are performed for the cryo-ET model (equation 2

), excluding the projection step. The metric used for comparison is the geodesic distance, as defined in equation (10)

. Here, g denotes the true rotation, $[{\hat g}_{\rm {MLE}}]$ represents the MLE estimator from equation (24)

and $[{\hat g}_{\rm {MMSE}}]$ denotes the Bayesian MMSE estimator from equation (21)

. In the high-SNR regime (σ → 0) the MLE and MMSE estimators converge, and the geodesic distance scales empirically as ∝ L^1/3. This scaling reflects the three-parameter nature of $[{\sf{SO}}(3)]$ rotations, where the resolution of the sampling grid improves as L increases. The results shown are based on Monte Carlo simulations with 3000 trials per data point.

STRUCTURAL
BIOLOGY

ISSN: 2059-7983

Volume 82| Part 4| April 2026| Pages 274-294

https://doi.org/10.1107/S2059798326001415

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