Abstract
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.
Original language | English |
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Article number | 31 |
Journal | Journal of Scientific Computing |
Volume | 95 |
Issue number | 1 |
Early online date | 8 Mar 2023 |
DOIs | |
Publication status | Published - 1 Apr 2023 |
Keywords
- Deep learning
- Inverse problems
- Direct sampling methods
- Diffusive optical tomography
- Reconstruction algorithm