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Solving Fourier Ptychographic Imaging Problems Via Neural Network Modeling and Tensorflow

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Solving Fourier Ptychographic Imaging Problems Via Neural Network Modeling and Tensorflow Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow SHAOWEI JIANG,1,3 KAIKAI GUO,1,3 JUN LIAO,1,3 AND GUOAN ZHENG1, 2* 1Biomedical Engineering, University of Connecticut, Storrs, CT, 06269, USA 2Electrical and Computer Engineering, University of Connecticut, Storrs, CT, 06269, USA 3These authors contributed equally to this work *[email protected] Abstract: Fourier ptychography is a recently developed imaging approach for large field-of- view and high-resolution microscopy. Here we model the Fourier ptychographic forward imaging process using a convolution neural network (CNN) and recover the complex object information in the network training process. In this approach, the input of the network is the point spread function in the spatial domain or the coherent transfer function in the Fourier domain. The object is treated as 2D learnable weights of a convolution or a multiplication layer. The output of the network is modeled as the loss function we aim to minimize. The batch size of the network corresponds to the number of captured low-resolution images in one forward / backward pass. We use a popular open-source machine learning library, TensorFlow, for setting up the network and conducting the optimization process. We analyze the performance of different learning rates, different solvers, and different batch sizes. It is shown that a large batch size with the Adam optimizer achieves the best performance in general. To accelerate the phase retrieval process, we also discuss a strategy to implement Fourier-magnitude projection using a multiplication neural network model. Since convolution and multiplication are the two most- common operations in imaging modeling, the reported approach may provide a new perspective to examine many coherent and incoherent systems. As a demonstration, we discuss the extensions of the reported networks for modeling single-pixel imaging and structured illumination microscopy (SIM). 4-frame resolution doubling is demonstrated using a neural network for SIM. The link between imaging systems and neural network modeling may enable the use of machine-learning hardware such as neural engine and tensor processing unit for accelerating the image reconstruction process. We have made our implementation code open- source for the broad research community. Key words: (100.4996) Pattern recognition, neural networks; (170.3010) Image reconstruction techniques; (170.0180) Microscopy. References and links 1. G. Zheng, R. Horstmeyer, and C. Yang, "Wide-field, high-resolution Fourier ptychographic microscopy," Nature Photonics 7, 739-745 (2013). 2. X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, "Quantitative phase imaging via Fourier ptychographic microscopy," Optics Letters 38, 4845-4848 (2013). 3. L. Tian, X. Li, K. 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