Fast post-processing algorithm for improving electrical capacitance tomography image reconstruction

Grebennikov, Alexandre; Gamio, Carlos

doi:10.1080/17415970500272874

Cited by 2 publications

(2 citation statements)

References 7 publications

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“…ET is very important in solution of such problems [2], particularly, in recognition of petroleum tube contents [3]. ET can be mathematically described for the plane domain as a coefficient inverse problem for the Laplace type equation, written in the divergent form [4].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of Space Distribution of Characteristics in Compound Structures by General Ray Method

Grebennikov

2014

MRS Proc.

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Recognition of material structures, particularly, identification of electrical properties of materials by Electrical Tomography is very important in different applied problems. In a plane case Electrical Tomography can be mathematically described as a coefficient inverse problem for the Laplace type equation, written in the divergent form. The General Ray (GR) Principle, proposed by the author, reduces the Laplace type equation to the family of ordinary differential equations with respect the traces of the potential function and the permittivity function on the lines, which intersect the plane domain. General Ray Principle was realized as General Ray method and fast algorithm for the plane domains. In presented investigation we apply the plane scheme of GR-method for some space domains to identify distribution of structure characteristics inside it. For this we consider the space domain as assemblage of plane slices. Reconstructing desired distribution in each plane slice we obtain then the space internal distribution of electrical characteristics by 3D spline approximation. We consider here specific variant of the measurement scheme for the 3D Electrical Tomography (ET), based on the variant, proposed by the author for the plane domain. Proposed approach gives, in principle, the possibility to use a large number of electrodes, obtain more values of the input data and reconstruct the desired space structure more perfectly. Computer simulation of this 3D scheme is realized as MATLAB software and justified by numerical experiments on simulated examples.

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Section: Introductionmentioning

confidence: 99%

Reconstruction of Space Distribution of Characteristics in Compound Structures by General Ray Method

Grebennikov

2014

MRS Proc.

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“…For some complex structures in the target field, it may be not enough to capture the main features by the immediate estimation of the proposed method. To this end, we use the post-processing based on the regularization [18] to improve the connectivity of main features. In general, the penalty term can be given by a quadratic form, which can achieve the global minimum with the convex constraint in the closed interval.…”

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confidence: 99%

Ensemble-based implicit sampling for Bayesian inverse problems with non-Gaussian priors

Ba¹,

Jiang²

2018

Preprint

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In the paper, we develop an ensemble-based implicit sampling method for Bayesian inverse problems. For Bayesian inference, the iterative ensemble smoother (IES) and implicit sampling are integrated to obtain importance ensemble samples, which build an importance density. The proposed method shares a similar idea to importance sampling. IES is used to approximate mean and covariance of a posterior distribution. This provides the MAP point and the inverse of Hessian matrix, which are necessary to construct the implicit map in implicit sampling. The importance samples are generated by the implicit map and the corresponding weights are the ratio between the importance density and posterior density. In the proposed method, we use the ensemble samples of IES to find the optimization solution of likelihood function and the inverse of Hessian matrix. This approach avoids the explicit computation for Jacobian matrix and Hessian matrix, which are very computationally expensive in high dimension spaces. To treat non-Gaussian models, discrete cosine transform and Gaussian mixture model are used to characterize the non-Gaussian priors. The ensemble-based implicit sampling method is extended to the non-Gaussian priors for exploring the posterior of unknowns in inverse problems. The proposed method is used for each individual Gaussian model in the Gaussian mixture model. The proposed approach substantially improves the applicability of implicit sampling method. A few numerical examples are presented to demonstrate the efficacy of the proposed method with applications of inverse problems for subsurface flow problems and anomalous diffusion models in porous media.

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Fast post-processing algorithm for improving electrical capacitance tomography image reconstruction

Cited by 2 publications

References 7 publications

Reconstruction of Space Distribution of Characteristics in Compound Structures by General Ray Method

Reconstruction of Space Distribution of Characteristics in Compound Structures by General Ray Method

Ensemble-based implicit sampling for Bayesian inverse problems with non-Gaussian priors

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