Search for: All records

Abstract Principal component analysis (PCA) plays an important role in the analysis of cryo-electron microscopy (cryo-EM) images for various tasks such as classification, denoising, compression, and ab initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-EM projection images affected by radial point spread functions that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier–Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions. For $ N $ images of size $ L\times L $ , our method has time complexity $ O\left({NL}^3+{L}^4\right) $ and space complexity $ O\left({NL}^2+{L}^3\right) $ . In contrast to previous work, these complexities are independent of the number of different contrast transfer functions of the images. We demonstrate our approach on synthetic and experimental data and show acceleration by factors of up to two orders of magnitude. 

We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle cryo-electron microscopy, we focus on the low signal-to-noise regime, where it is difficult to estimate the locations and orientations of the target images in the measurement. Our approach uses autocorrelation analysis to estimate rotationally and translationally invariant features of the target image. We demonstrate that, regardless of the level of noise, our technique can be used to recover the target image when the measurement is sufficiently large.