  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.
