Learn an index operator by CNN for solving diffusive optical tomography: a deep direct sampling method

TL;DR

This paper introduces a deep learning-based method called DDSM that uses CNNs to improve the reconstruction of inhomogeneous inclusions in diffusive optical tomography, especially with limited boundary data and noise.

Contribution

The paper develops a novel deep direct sampling method employing CNNs to enhance DOT reconstruction accuracy and robustness, integrating multiple measurements efficiently.

Findings

Improved reconstruction accuracy with limited boundary data.

Enhanced robustness against noise in measurements.

Fast and easy implementation of the proposed method.

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), 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.