QUANTIFICATION OF MODEL BIAS UNDERLYING THE PHENOMENON OF "EINSTEIN FROM NOISE"
STATISTICA SINICA(2021)
摘要
Arising from cryogenic electron microscopy image analysis, "Einstein from noise" refers to spurious patterns that can emerge as a result of averaging a large number of white-noise images aligned to a reference image through rotation and translation. Although this phenomenon is often attributed to model bias, quantitative studies on such bias are lacking. Here, we introduce a simple framework under which an image of p pixels is treated as a vector of dimension p, and a white-noise image is a random vector uniformly sampled from the (p - 1)-dimensional unit sphere. Moreover, we adopt the cross-correlation of two images, which is a similarity measure based on the dot product of image pixels. This framework explains geometrically how the bias results from averaging a properly chosen set of white-noise images that are most highly cross-correlated with the reference image. We quantify the bias in terms of three parameters: the number of white-noise images (n), the image dimension (p), and the size of the selection set (m). Under the conditions that n, p, and m are all large and (ln n)(2)/p and m/n are both small, we show that the bias is approximately root 2 gamma/(1 + 2 gamma), where gamma = (m/p) ln (n/m).
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关键词
Cross correlation, cryogenic electron microscopy, extreme value distribution, high dimensional data analysis, model bias, white-noise image
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