Complex imaging of phase domains by deep neural networks

Machine-learning approaches can greatly facilitate single-particle-imaging experiments at X-ray free-electron-laser facilities by providing real-time images from the coherent X-ray diffraction data stream, using methods presented in this article.
The reconstruction of a single-particle image from the modulus of its Fourier transform, by phase-retrieval methods, has been extensively applied in X-ray structural science. Particularly for strong-phase objects, such as the phase domains found inside crystals by Bragg coherent diffraction imaging (BCDI), conventional iteration methods are time consuming and sensitive to their initial guess because of their iterative nature. Here, a deep-neural-network model is presented which gives a fast and accurate estimate of the complex single-particle image in the form of a universal approximator learned from synthetic data. A way to combine the deep-neural-network model with conventional iterative methods is then presented to refine the accuracy of the reconstructed results from the proposed deep-neural-network model. Improved convergence is also demonstrated with experimental BCDI data.