Soft-voting for robust common line assessment in cryo-EM angular reconstruction

Single-particle cryo-electron microscopy (cryo-EM) reconstructs three-dimensional (3D) macromolecular structures from two-dimensional (2D) projection images acquired at unknown orientations. Common line-based angular reconstruction estimates projection orientations from pairwise common lines, but reliable common line detection remains challenging at the low signal-to-noise ratios (SNRs) typical of cryo-EM experiments. Existing voting-based approaches either assign equal weight to all votes or apply hard binary thresholds, thereby discarding valuable confidence information and limiting orientation estimation accuracy. We present Soft-Voting, a common line assessment framework that replaces binary vote weighting with continuous confidence weighting. For each projection pair, Soft-Voting constructs a consensus histogram of candidate dihedral angles using information from all remaining projections, with each vote weighted according to the reliability of its supporting common lines. The resulting common-line reliability scores are used to construct pairwise weights for spherical embedding, enabling globally consistent orientation recovery. Experiments on a synthetic dataset (EMD-33026) with SNRs ranging from 1 to 1/16 show that Soft-Voting generally achieves lower orientation errors than existing common line-based methods, especially under low-SNR conditions. Experiments on three real cryo-EM datasets (EMPIAR-10028, EMPIAR-10328, and EMPIAR-10455) further show that Soft-Voting produces competitive ab initio reconstructions based on Fourier shell correlation against reference maps. The results indicate that Soft-Voting can improve common-line assessment and the robustness of cryo-EM angular reconstruction, particularly under challenging low-SNR conditions.