  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.
