Online learning in optical tomography: A stochastic approach


Journal Article

© 2018 IOP Publishing Ltd. We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the incoming-outgoing pair of light intensity. We formulate it as a PDE-constraint optimization problem, where the mismatch of computed and measured outgoing data is minimized with same initial data and RTE constraint. The memory and computation cost it requires, however, is typically prohibitive, especially in high dimensional space. Smart iterative solvers that only use partial information in each step is called for thereafter. Stochastic gradient descent method is an online learning algorithm that randomly selects data for minimizing the mismatch. It requires minimum memory and computation, and advances fast, therefore perfectly serves the purpose. In this paper we formulate the problem, in both nonlinear and its linearized setting, apply SGD algorithm and analyze the convergence performance.

Full Text

Duke Authors

Cited Authors

  • Chen, K; Li, Q; Liu, JG

Published Date

  • May 29, 2018

Published In

Volume / Issue

  • 34 / 7

Electronic International Standard Serial Number (EISSN)

  • 1361-6420

International Standard Serial Number (ISSN)

  • 0266-5611

Digital Object Identifier (DOI)

  • 10.1088/1361-6420/aac220

Citation Source

  • Scopus