Online learning in optical tomography: a stochastic approach. (29th May 2018)

• Record Type: Journal Article
• Authors: Chen, Ke; Li, Qin; Liu, Jian-Guo
• Is Part Of: Inverse problems. Volume 34:Number 7(2018:Jul.)
• Publication Date: 2018-05-29
• Subjects: stochastic gradient descent -- radiative transfer equation -- optical tomography -- online learning; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aac220
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.