用CNN学习指数算子求解扩散光学层析成像：一种深度直接采样方法
Learn an index operator by CNN for solving diffusive optical tomography: a deep direct sampling method
摘要：
在这项工作中，我们调查的情况下，有限的边界测量扩散光学层析成像（DOT）的问题。受直接取样法（DSM）的启发，我们发展了一种深部直接取样法（DDSM）来恢复埋藏在均匀背景中的非均匀包裹体。在这种方法中，我们设计了一个卷积神经网络（CNN）来近似模拟底层数学结构的索引函数。所提出的DDSM的好处包括快速和容易的实施，将多个测量，以获得高质量的重建，和先进的鲁棒性对噪声的能力。数值实验表明，该算法在不降低效率的前提下提高了重建精度，显示了其解决实际DOT问题的潜力。
英文摘要：
In this work, we investigate the diffusive optical tomography (DOT) problem in the case that limited boundary measurements are available. Motivated by the direct sampling method (DSM), we develop a deep direct sampling method (DDSM) to recover the inhomogeneous inclusions buried in a homogeneous background. In this method, we design a convolutional neural network (CNN) to approximate the index functional that mimics the underling mathematical structure. The benefits of the proposed DDSM include fast and easy implementation, capability of incorporating multiple measurements to attain high-quality reconstruction, and advanced robustness against the noise. Numerical experiments show that the reconstruction accuracy is improved without degrading the efficiency, demonstrating its potential for solving the real-world DOT problems.
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