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.

翻译：在这项工作中,我们调查在有有限的边界测量的情况下的光学断层成像(DOT)问题,在直接取样方法的推动下,我们开发了一种深度直接取样方法(DMSM),以恢复埋藏在同质背景中的不相容结合物。在这个方法中,我们设计了一个革命神经网络(CNN),以近似模拟数学结构下的指数功能。拟议的DMS的优点包括快速和易于执行、采用多种测量来进行高质量重建的能力和对噪音的高度稳健性。数字实验表明,重建的准确性在不降低效率的情况下得到了提高,显示了它解决现实世界DOT问题的潜力。