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In this work, we investigate the diffusive optical tomography (DOT) problemin the case that limited boundary measurements are available. Motivated by thedirect sampling method (DSM), we develop a deep direct sampling method (DDSM)to recover the inhomogeneous inclusions buried in a homogeneous background. Inthis method, we design a convolutional neural network (CNN) to approximate theindex functional that mimics the underling mathematical structure. The benefitsof the proposed DDSM include fast and easy implementation, capability ofincorporating multiple measurements to attain high-quality reconstruction, andadvanced robustness against the noise. Numerical experiments show that thereconstruction accuracy is improved without degrading the efficiency,demonstrating its potential for solving the real-world DOT problems.

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