Inverse Problem for Electromagnetic Propagation in a Dielectric Medium using Markov Chain Monte Carlo Method

Knopp, Jeremy S.; Kojima, Fumio

doi:10.5687/sss.2011.208

Cited by 7 publications

(8 citation statements)

References 4 publications

(4 reference statements)

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“…(12) and (13) from which sample paths can be drawn using Markov chains. For the practical implementation of MCMC, Metropolis-Hasting algorithm is applied to the problem considered here ( See [14] ).…”

Section: Stochastic Inverse Analysismentioning

confidence: 99%

“…Recently, interest has grown in stochastic inversion using Markov Chain Monte Carlo (MCMC) methods [8] [9]. Some previous efforts on the similar approach has been proposed in [10], [11]. The method has great advantages for the more practical aspects of inversions such as setting initial guesses and overcoming local minimums of the inverse solution.…”

Section: Introductionmentioning

confidence: 99%

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Quantitative Evaluation for Two-dimensional Electromagnetic Propagation in a Dielectric Medium using Markov Chain Monte Carlo Method

Kojima

Knopp

2012

Stochastic Systems Theory and its Applications (SSS)

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Motivated by quantitative evaluation of aging properties of electrical cables, a computational method for identifying physical parameters of dielectric materials is considered. First, a nondestructive testing using microwaveguide is described by electric and magnetic fields defined on the problem. Secondly, an inversion technique based on Markov Chain Monte Carlo method (MCMC) is employed for solving the electromagnetic interrogation treated here. Finally, a numerical scheme of the direct problem is developed using the finitedifference time-domain method (FDTD) in two spatial dimensions. Applying Metropolis-Hasting algorithm to the inversion presented here, results on computational experiments are demonstrated in order to show the feasibility and applicability of the proposed method.

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Section: Stochastic Inverse Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantitative Evaluation for Two-dimensional Electromagnetic Propagation in a Dielectric Medium using Markov Chain Monte Carlo Method

Kojima

Knopp

2012

Stochastic Systems Theory and its Applications (SSS)

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“…These methods entail treatment of individual parameters as random variables to be estimated from data on the prescribed nondestructive tests. Our prior efforts on material characterizations have been concentrated on stationary frequency response of dielectric materials using independent Metropolis-Hastings [3], gPC Galerkin method [4], and the stochastic spline Galerkin method [5]. In this paper, our concern for material interrogation methods is motivated by a dynamically varying signal response model using Hamiltonian Monte Carlo method (HMC) [6].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Inversion for Electromagnetic Propagation in a Dielectric Medium using Hamiltonian Monte Carlo Method

Kojima

2016

Stochastic Systems Theory and its Applications (SSS)

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This paper is concerned with material interrogation methods for homogeneous dielectric materials using stochastic inversion. Frequency dispersions for homogeneous dielectric materials can be described by the Debye formulation. Propagation in the dielectric medium is assumed to be governed by the timedependent Maxwell's equations in one spatial dimension. When a plane wave travelling in the free space hits the dielectric material, the reflective wave from the front edge of material is measurable at the free space. Thus the problem considered here is to quantify uncertainties of the estimated dielectric parameters from the measurements of electric field. A computational method using Hamiltonian Monte Carlo sampling based on nonlinear hierarchical models is tested.

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“…A solution to the inverse problem can generally be divided into two types. One is a statistical method, e.g., a Monte Carlo [26,27] or Bayesian [28,29] method. The other is optimization using a least-squares criterion [18,19,30,31], a regularization method [18][19][20][21][22][23], a level set method [32,33], etc.…”

Section: Introductionmentioning

confidence: 99%

Probability method for Cerenkov luminescence tomography based on conformance error minimization

Ding¹,

Wang²,

Jie³

et al. 2014

Biomed. Opt. Express

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Cerenkov luminescence tomography (CLT) was developed to reconstruct a three-dimensional (3D) distribution of radioactive probes inside a living animal. Reconstruction methods are generally performed within a unique framework by searching for the optimum solution. However, the ill-posed aspect of the inverse problem usually results in the reconstruction being non-robust. In addition, the reconstructed result may not match reality since the difference between the highest and lowest uptakes of the resulting radiotracers may be considerably large, therefore the biological significance is lost. In this paper, based on the minimization of a conformance error, a probability method is proposed that consists of qualitative and quantitative modules. The proposed method first pinpoints the organ that contains the light source. Next, we developed a 0-1 linear optimization subject to a space constraint to model the CLT inverse problem, which was transformed into a forward problem by employing a region growing method to solve the optimization. After running through all of the elements used to grow the sources, a source sequence was obtained. Finally, the probability of each discrete node being the light source inside the organ was reconstructed. One numerical study and two in vivo experiments were conducted to verify the performance of the proposed algorithm, and comparisons were carried out using the hp-finite element method (hp-FEM). The results suggested that our proposed probability method was more robust and reasonable than hp-FEM.

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Inverse Problem for Electromagnetic Propagation in a Dielectric Medium using Markov Chain Monte Carlo Method

Cited by 7 publications

References 4 publications

Quantitative Evaluation for Two-dimensional Electromagnetic Propagation in a Dielectric Medium using Markov Chain Monte Carlo Method

Quantitative Evaluation for Two-dimensional Electromagnetic Propagation in a Dielectric Medium using Markov Chain Monte Carlo Method

Stochastic Inversion for Electromagnetic Propagation in a Dielectric Medium using Hamiltonian Monte Carlo Method

Probability method for Cerenkov luminescence tomography based on conformance error minimization

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