Coherent diffractive imaging (CDI) is a promising technique that takes advantage of the diffraction of a light beam or an electron to reconstruct the image of a sample eliminating the need for optics. The method has numerous applications ranging from nanoscale imaging to X-ray ptychography and astronomical wavefront configurations. However, one of the main problems with CDI is the phase recovery problem, where the detectors do not record the phase of the diffracted wave, causing a loss of information.
A considerable amount of research has been conducted to address this problem, primarily focusing on the use of artificial neural networks. Although these methods are much more efficient than conventional iterative methods, they require a large volume of labeled data for training, which is experimentally cumbersome. Furthermore, these methods also lead to degraded reconstructed image quality, which requires better focusing. Therefore, the authors of this research paper from SLAC National Accelerator Laboratory, USA, have introduced PtychoPINN. This unsupervised neural network reconstruction method retains significant speed over previous deep learning-based methods while improving quality.
Conventional physics-based CDI methods are accurate but computationally expensive as they are iterative in nature. In contrast, neural network-based methods rely on a large training data set to capture particular data regularities well and have better reconstruction speed. Therefore, researchers have tried to incorporate the advantages of both methods to create PtychoPINN. The researchers defined the model's loss function on the output of the forward-mapped neural network, forcing the network to learn diffraction physics.
PtychoPINN leverages an autoencoder architecture that incorporates convolutional, average pooling, upsampling, and custom layers to scale the input and output. The researchers used the output of the Poisson model and the corresponding negative log-likelihood objective, which modeled the intrinsic Poisson noise in the experimental data. Three different types of data sets were used to train and evaluate the model: 'Lines' for randomly oriented lines, Gaussian Random Field (GRF) and 'Large Features' for experimentally derived data. Each data set is based on sharpness, isotropy, and characteristic length in the real-space structure, and for each of them, the researchers simulated a collection of diffraction patterns corresponding to a rectangular grid of scan points in the sample and a known probe function.
The researchers compared the performance of PtychoPINN with the supervised learning benchmark PytchoNN. The former shows minimal phase and amplitude degradation in real space, while the latter experiences significant blurring. Furthermore, PytchoPINN also demonstrated a better maximum signal-to-noise ratio (PSNR). Although both performed well, when evaluated against the “Large Features” amplitude reconstruction, PytchoPINN outperformed the other with better Fourier ring correlation at the 50% threshold (FRC50).
In conclusion, PytchoPINN is an autoencoder framework for coherent diffractive imaging, in which researchers have incorporated physical principles to improve accuracy, resolution, and generalization, while requiring less training data. The framework significantly outperforms the PytchoNN supervised learning baseline on metrics such as PSNR and FCR50. Although it is a promising tool, it is still far from perfect and researchers are working to continue improving its capabilities. Nonetheless, the framework is a promising tool and has the potential to be used for high-resolution real-time imaging that exceeds the resolution of lens-based systems without compromising imaging performance.
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