An encryption–decryption framework to validating single-particle imaging

Abstract

We propose an encryption–decryption framework for validating diffraction intensity volumes reconstructed using single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) when the ground truth volume is absent. This conceptual framework exploits each reconstructed volumes’ ability to decipher latent variables (e.g. orientations) of unseen sentinel diffraction patterns. Using this framework, we quantify novel measures of orientation disconcurrence, inconsistency, and disagreement between the decryptions by two independently reconstructed volumes. We also study how these measures can be used to define data sufficiency and its relation to spatial resolution, and the practical consequences of focusing XFEL pulses to smaller foci. This conceptual framework overcomes critical ambiguities in using Fourier Shell Correlation (FSC) as a validation measure for SPI. Finally, we show how this encryption-decryption framework naturally leads to an information-theoretic reformulation of the resolving power of XFEL-SPI, which we hope will lead to principled frameworks for experiment and instrument design.

High-Throughput 3D Ensemble Characterization of Individual Core–Shell Nanoparticles with X-ray Free Electron Laser Single-Particle Imaging

“…The angular correlation map was obtained by calculating the cross-correlation between the orientation posterior probability distributions of 2D diffraction. The rotational cross-correlation ξ rot is where Ω, K , and W are the 3D rotation, 2D diffraction pattern, and 3D model, respectively, and Ω′ is the relative 3D rotation in the cross-correlation . The angular correlation ξ ang (θ| K , W ) is then obtained by summing the correlation values of 3D rotations with the same angle of rotation.…”

“…where Ω, K, and W are the 3D rotation, 2D diffraction pattern, and 3D model, respectively, and Ω′ is the relative 3D rotation in the crosscorrelation. 54 The angular correlation ξ ang (θ|K, W) is then obtained by summing the correlation values of 3D rotations with the same angle of rotation. An n-fold rotational symmetry results in high crosscorrelation at rotation angles of 2π/n, and these peaks are prominent for the majority of patterns for each 3D volume (Figure S4).…”

Comparison of EMC and CM methods for orienting diffraction images in single-particle imaging experiments

“…This and some other methods (Yoon et al, 2016;Liu et al, 2018) rely on dividing the measured dataset into two or more parts and compare the independently recovered intensity distributions. However, Shen et al (2021) have shown that these methods suffer from serious problems. Most notably, the correlation can grow with increasing orientation disorder when approaching the powder average.…”

“…We can investigate the loss off resolution by calculating the FSC between the 3D intensity volume W reconstructed by either method and the ideally reconstructed intensity W T or the noiseless 3D model intensity distribution W 0 . We noted earlier that FSC, calculated between volumes reconstructed from two independent sets of measured data, suffers serious problems when used for characterization of the resolution errors (Shen et al, 2021). However, when FSC is calculated between a measured intensity volume W and model intensities W 0 with no errors or W T with well known errors (Poisson noise and interpolation The maximums of Pearson correlation between intensity volumes W x and W y as rotated relative to each other, for lysozyme (right) and RNA polymerase II (left) at various incident XFEL fluence values.…”

Gallium Nitride Metalens for Image Decryption

“…There is obviously a need to develop secure image methods in order to assure the safety of image transmission [1][2][3][4][5]. As a result, a secure method for encryption and decryption of digital images, well-known as cryptography, is developed thanks to the development of digital communication [6,7].…”