A partially reflecting random walk on spheres algorithm for electrical impedance tomography

Journal Article · Tue Dec 15 04:00:00 EST 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2015.10.005· OSTI ID:22570204

Maire, Sylvain ^[1]; Simon, Martin ^[2]

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1. Laboratoire LSIS Equipe Signal et Image, Université du Sud Toulon-Var, Av. Georges Pompidou, BP 56, 83162 La Valette du Var Cedex (France)
2. Institute of Mathematics, Johannes Gutenberg University, 55099 Mainz (Germany)

In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias and the variance of the new estimator both theoretically and experimentally. Subsequently, the variance of the new estimator is considerably reduced via a novel control variate conditional sampling technique which yields a highly efficient hybrid forward solver coupling probabilistic and deterministic algorithms.

• OSTI ID: 22570204
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 303; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
BOUNDARY CONDITIONS
BROWNIAN MOVEMENT
DETERMINISTIC ESTIMATION
DIFFUSION
ELECTRIC POTENTIAL
GRAPH THEORY
INTERFACES
MONTE CARLO METHOD
PROBABILISTIC ESTIMATION
RANDOMNESS
SPHERES
TOMOGRAPHY