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Abstract

Single-particle imaging (SPI) at x-ray free-electron lasers is a technique to determine the three-dimensional structure of nanoscale objects like biomolecules from a large number of diffraction patterns of copies of these objects in random orientations. The technique has been limited to relatively low resolution due to background noise and heterogeneity of the target particles. A recently introduced reference-enhanced holographic SPI methodology uses strongly scattering holographic references to improve background tolerance, and, thus, the achievable resolution, at the cost of additional latent variables beyond orientation. Here, we describe an improved reconstruction algorithm based on maximum likelihood estimation, which scales better, enabling fine sampling of latent parameters to reach high resolutions, and much better performance in the low signal limit. Furthermore, we show that structural variations within the target particle are averaged in real space, significantly improving robustness to conformational heterogeneity in comparison to conventional SPI. With these computational improvements, we believe reference-enhanced SPI is capable of reaching sub-nanometer resolution biomolecule imaging.