Structure from Noise: Confirmation Bias in Particle Picking in Structural Biology

The computational pipelines of single-particle cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET) include an early particle-picking stage, in which a micrograph or tomogram is scanned to extract candidate particles, typically via template matching or deep-learning-based techniques. The extracted particles are then passed to downstream tasks such as classification and 3D reconstruction. Although it is well understood empirically that particle picking can be sensitive to the choice of templates or learned priors, a quantitative theory of the bias introduced by this stage has been lacking. Here, we develop a mathematical framework for analyzing bias in template matching-based detection with concrete applications to cryo-EM and cryo-ET. We study this bias through two downstream tasks: (i) maximum-likelihood estimation of class means in a Gaussian mixture model and (ii) 3D volume reconstruction from the extracted particle stack. We show that when template matching is applied to pure noise, then under broad noise models, the resulting maximum-likelihood estimates converge asymptotically to deterministic, noise-dependent transforms of the user-specified templates, yielding a structure from noise effect. We further characterize how the resulting bias depends on the noise statistics, sample size, dimension, and detection threshold. Finally, controlled experiments using standard cryo-EM software corroborate the theory, demonstrating reproducible structure from noise artifacts in low-SNR data.