A model bias problem arising from image analysis in cryogenic electron microscopy

Yi-Ching Yao

Institute of Statistical Science

Academia Sinica

yao@stat.sinica.edu

Cryogenic electron microscopy (cryo-EM) is an imaging technique to construct the 3D structures of biological samples such as membrane proteins. In some cases, the extremely low signal-to-noise ratio of cryo-EM images results in the processing dictated by the reference of a model, which is known as model bias. A well-known example showed that a blurred Einstein face emerged from 1000 aligned images of pure noise (often referred as “Einstein from noise”). To investigate this model bias phenomenon quantitatively, we consider a simplified model consisting of `n` iid `p`-dimensional images of pure Gaussian noise and a specified reference image (of Einstein). The `n` images of pure noise are sorted in terms of their cross correlation values with the reference image, and the top `m` images (of pure noise) are selected and averaged. We derive asymptotic distributions for the cross correlation between the averaged image and the reference image as `n,p,m\to\infty` at suitable rates. (This is joint work with Shao-Hsuan Wang, Wei-Hau Chang and I-Ping Tu.)Keyword: Digital image, noise, correlation, asymptotic distribution