Learn an Index Operator by CNN for Solving Diffusive Optical Tomography: A Deep Direct Sampling Method
Learn an Index Operator by CNN for Solving Diffusive Optical Tomography: A Deep Direct Sampling Method
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DOI：
10.1007/s10915-023-02115-7
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发表时间：
2021-04
影响因子：
2.5
通讯作者：
Ruchi Guo;Jiahua Jiang;Yi Li
中科院分区：
文献类型：
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作者：
Ruchi Guo;Jiahua Jiang;Yi Li
在这项工作中，我们研究了可用边界测量有限的情况下的扩散光学断层扫描（DOT）问题。受到 Chow 等人提出的直接采样方法 (DSM) 的启发。 (SIAM J Sci Comput 37(4):A1658–A1684, 2015)，我们开发了一种深度直接采样方法（DDSM）来恢复埋藏在均匀背景中的不均匀夹杂物。在这种方法中，我们设计了一个卷积神经网络来近似模仿底层数学结构的索引函数。所提出的 DDSM 的优点包括快速且轻松的实施、合并多个测量以获得高质量重建的能力以及针对噪声的高级鲁棒性。数值实验表明，在不降低效率的情况下提高了重建精度，展示了其解决现实世界 DOT 问题的潜力。
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) proposed in Chow et al. (SIAM J Sci Comput 37(4):A1658–A1684, 2015), 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 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.