用神经网络建模和TensorFlow求解傅立叶重叠关联成像问题
Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow
摘要：
傅立叶重叠关联成像是近年来发展起来的一种大视场、高分辨率显微成像方法。在这里，我们使用卷积神经网络（CNN）的傅立叶重叠关联成像的前向成像过程建模和恢复复杂的目标信息在网络的训练过程。在这种方法中，网络的输入是空间域中的点扩散函数或傅立叶域中的相干传递函数。对象被视为卷积或乘法层的2D可学习权重。网络的输出被建模为我们的目标是最小化的损失函数。网络的批量大小对应于在一次向前/向后传递中捕获的低分辨率图像的数量。我们使用流行的开源机器学习库TensorFlow来设置网络并进行优化过程。我们分析了不同学习率、不同求解器和不同批量大小的性能。结果表明，一个大的批量大小与亚当优化器实现了最佳的性能一般。为了加速相位恢复过程，我们还讨论了一种策略，实现傅立叶幅度投影使用乘法神经网络模型。由于卷积和乘法是成像建模中最常见的两种运算，因此本文的方法可以为研究许多相干和非相干系统提供一个新的视角。作为演示，我们讨论了扩展的报告网络建模单像素成像和结构照明显微镜（SIM）。4-使用SIM的神经网络来证明帧分辨率加倍。我们已经为广泛的研究社区开放了我们的实现代码。
英文摘要：
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. We have made our implementation code open-source for the broad research community.
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