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

Figure 4
Comparison of 2D image recovery using the MMSE and MLE rotation estimators. Iterative image-recovery procedures with the MMSE estimator ( $[{\hat g}_{\rm {MMSE}}]$ ) and MLE estimator ( $[{\hat g}_{\rm {MLE}}]$ ) are defined in equations (31)

and (32)

, respectively. The experiment employs a template image of Einstein and a ground-truth image of Newton, both rotated in 2D over a uniform polar grid with L = 30 samples. Each image is of size 100 × 100 pixels, and the radial direction is discretized using R = 300 points. The reconstructed images within the dark-orange rectangle (right panel) show superior performance with the MMSE rotation estimator, with Pearson cross-correlation (PCC) provided for each reconstructed image. The MLE and MMSE reconstructions are nearly identical at high SNR (σ → 0), as predicted by Proposition 2

. The SNR values used for the panels (from right to left) are 10⁻², 4 × 10⁻³, 2 × 10⁻³, 7 × 10⁻⁴ and 2 × 10⁻⁴. At very low SNR (σ → ∞) the `Einstein from Noise' effect appears, where the estimator resembles the template image of Einstein rather than the underlying truth of Newton. In intermediate SNR ranges, using the MMSE estimator in the iterative step clearly outperforms the MLE estimator.

STRUCTURAL
BIOLOGY

ISSN: 2059-7983

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

https://doi.org/10.1107/S2059798326001415

Open

access

Search IUCr Journals		doi		Advanced search
Author		volume	page