Learn an Index Operator by CNN for Solving Diffusive Optical Tomography: A Deep Direct Sampling Method

Ruchi Guo, Jiahua Jiang*, Yi Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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 languageEnglish
Article number31
JournalJournal of Scientific Computing
Volume95
Issue number1
Early online date8 Mar 2023
DOIs
Publication statusPublished - 1 Apr 2023

Keywords

  • Deep learning
  • Inverse problems
  • Direct sampling methods
  • Diffusive optical tomography
  • Reconstruction algorithm

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