![]() However, so far, most of the proposed neural networks employ a supervised learning approach, matching input diffraction patterns in reciprocal space to output particle morphological information in real space, which usually needs large training datasets to train the neural network so that it can represent a universal approximation function. Meanwhile, an adaptive ML-based approach for 3D phase retrieval has been demonstrated by using spherical harmonics. There has been rapid progress for 2-dimensional (2D) phase retrieval using convolutional neural networks (CNN) recently. Because these methods are based on projections, the calculated error usually is only used to monitor the convergence and rarely used as feedback to adjust the related algorithmic parameters, which makes these methods sensitive to their initialization conditions.įor phase retrieval, deep-neural-network-based ML methods have recently shown a significant advantage in providing rapid reconstruction results in a CDI experiment. Thus, when inverting coherent X-ray diffraction patterns, conventional iterative methods typically need thousands of iterations and switch algorithms to confidently converge to a reproducible solution and require tuning of many algorithmic parameters and expert strategies. However, for experimental data with inherent noise, these projection-based methods are found to struggle with local minima, which leads to an ambiguous, rather than unique, solution. Theoretically, for a finite object, when the modulus of its Fourier Transform is well oversampled, a unique solution is guaranteed for these methods. In general, these iterative phase retrieval methods can be expressed as successive projections. Until now, the extensively used approach for CDI phase retrieval is the iterative methods, such as the hybrid input-output (HIO) method by Fienup, the difference map (DM) by Elser, and the relaxed averaged alternating reflection (RAAR) method by Luke. Due to the lost phase information in measured coherent X-ray diffraction signals, it is necessary to use phase retrieval as a key component of CDI, to reconstruct the real-space 3D images with morphological details from the measured signals. As modern X-ray sources, such as diffraction-limited storage rings and fourth-generation X-ray free-electron lasers, are developing worldwide to provide higher coherent flux densities, time-resolved and in-situ CDI experiments for single-particle imaging are becoming more and more capable to explore small particles’ dynamical phenomena such as driven melting, thermal fluctuation, driven phase transitions, catalysis, and high-pressure phenomena. Particularly, Bragg CDI has emerged as a promising technique for 3D strain imaging of crystalline particles. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms.Ĭoherent X-ray diffraction imaging (CDI) has been widely utilized to characterize the internal three-dimensional (3D) structure of single particles. More significantly, the proposed ML model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate ‘loss function’ alone. The trained ML model can rapidly provide an immediate result with high accuracy which could benefit real-time experiments, and the predicted result can be further refined with transfer learning. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. ![]() As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. ![]()
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