6533b85bfe1ef96bd12bb4d2
RESEARCH PRODUCT
A partially reflecting random walk on spheres algorithm for electrical impedance tomography
Sylvain MaireMartin Simonsubject
Physics and Astronomy (miscellaneous)random diffusion coefficientvariance reductionMonte Carlo method010103 numerical & computational mathematicsControl variates01 natural sciencesdiscontinuous diffusion coefficientrandom walk on spheresFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Mathematics - Numerical Analysis0101 mathematicsElectrical impedance tomographyMathematicsNumerical AnalysisApplied MathematicsProbabilistic logicEstimatorMonte Carlo methodsreflecting Brownian motionNumerical Analysis (math.NA)Inverse problemRandom walkComputer Science Applications010101 applied mathematicsComputational MathematicsModeling and SimulationVariance reductionAlgorithmelectrical impedance tomographydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-12-15 | Journal of Computational Physics |