Abstract
One of the outstanding analytical problems in X-ray single-particle imaging (SPI) is the classification of structural heterogeneity, which is especially difficult given the low signal-to-noise ratios of individual patterns and the fact that even identical objects can yield patterns that vary greatly when orientation is taken into consideration. Proposed here are two methods which explicitly account for this orientation-induced variation and can robustly determine the structural landscape of a sample ensemble. The first, termed common-line principal component analysis (PCA), provides a rough classification which is essentially parameter free and can be run automatically on any SPI dataset. The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand-maximize-compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern. Both discrete structural classes and continuous deformations are recovered. These developments diverge from previous approaches of extracting reproducible subsets of patterns from a dataset and open up the possibility of moving beyond the study of homogeneous sample sets to addressing open questions on topics such as nanocrystal growth and dynamics, as well as phase transitions which have not been externally triggered.
Highlights
The second method, utilizing variation auto-encoders (VAEs), can generate 3D structures of the objects at any point in the structural landscape. Both these methods are implemented in combination with the noise-tolerant expand–maximize– compress (EMC) algorithm and its utility is demonstrated by applying it to an experimental dataset from gold nanoparticles with only a few thousand photons per pattern
The dataset discussed in the rest of this work was collected as part of the experiment described by Ayyer et al (2021), which we review in brief: The single-particle imaging (SPI) experiment was performed with the megahertz-rate European XFEL (Decking et al, 2020) on the SPB/SFX instrument (Mancuso et al, 2019) with 6 keV photons in pulses with an average energy of 2.5 mJ (2.6 Â 1012 photons) measured upstream of the focusing optics
Part of the dataset was collected with the European XFEL running at an intra-train repetition rate of 2 of 11 Yulong Zhuang et al Machine learning for sample characterization
Summary
X-ray single-particle imaging (SPI) is a method to reconstruct 3D structures of isolated nanoscale objects by collecting a large number of diffraction patterns using bright X-ray pulses. The framework used for this classification can be used to study datasets where the heterogeneity is not just a drawback, uncovering the landscape of structural variations in the sample. This requires the detection of discrete classes of object shapes representing contaminants, aggregates etc. The second is a generative method using variational auto-encoders (VAEs) which enables us to visualize the 3D structure of the particle at any point along its landscape Both methods are applied to the dataset to study the continuous XFEL-induced deformation of the cubic nanoparticles to spheres
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