Skip to Main content Skip to Navigation
Journal articles

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

Sylvain Maire 1 Martin Simon 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : 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. In a second step, the variance is considerably reduced via a novel control variate conditional sampling technique.
Document type :
Journal articles
Complete list of metadata

Cited literature [44 references]  Display  Hide  Download

https://hal.inria.fr/hal-01253538
Contributor : Sylvain Maire <>
Submitted on : Wednesday, January 13, 2016 - 8:20:11 PM
Last modification on : Tuesday, May 18, 2021 - 2:32:02 PM
Long-term archiving on: : Thursday, November 10, 2016 - 10:41:09 PM

File

PRWOS.pdf
Files produced by the author(s)

Identifiers

Citation

Sylvain Maire, Martin Simon. A partially reflecting random walk on spheres algorithm for electrical impedance tomography. Journal of Computational Physics, Elsevier, 2015, 303, ⟨10.1016/j.jcp.2015.10.005⟩. ⟨hal-01253538⟩

Share

Metrics

Record views

402

Files downloads

469