A Bayesian approach to improving the Born approximation for inverse scattering with high-contrast materials

Kaipio, Jari P.; Huttunen, Tomi; Luostari, Teemu; Lähivaara, Timo; Monk, Peter

doi:10.1088/1361-6420/ab15f3

Cited by 15 publications

(23 citation statements)

References 36 publications

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“…Thus, one way to improve the reconstructions is by using the Bayesian inversion approach in conjunction with the approximation error scheme [4] which can accommodate statistics of these errors resulting in better estimates. Therefore, a Bayesian approximation error [47] scheme will be employed to further improve the microwave tomography estimation. In the industrial drying system, the foam temperature will be higher than the room temperature at the exit.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Correlated Sample-Based Prior in Bayesian Inversion Framework for Microwave Tomography

Yadav

Omrani

Link

et al. 2022

IEEE Trans. Antennas Propagat.

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When using the statistical inversion framework in microwave tomography (MWT), generally the real and imaginary parts of the unknown dielectric constant are treated as uncorrelated and independent random variables. Thereby, in the maximum a posteriori estimates the two recovered variables may show different structural changes inside the imaging domain. In this work, a correlated sample-based prior model is presented to incorporate the correlation of the real part with the imaginary part of the dielectric constant in the statistical inversion framework. The method is used to estimate the inhomogeneous moisture distribution (as dielectric constant) in a large crosssection of a polymer foam. The targeted application of MWT is in industrial drying to derive intelligent control methods based on tomographic inputs for selective heating purposes. One of the features of the proposed method shows how to integrate lab-based dielectric characterization, often available in MWT application cases, in the prior modeling. The method is validated with numerical and experimental MWT data for the considered moisture distributions.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Correlated Sample-Based Prior in Bayesian Inversion Framework for Microwave Tomography

Yadav

Omrani

Link

et al. 2022

IEEE Trans. Antennas Propagat.

Self Cite

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“…The main idea of the Bayesian approximation error (BAE) approach is to replace the accurate forward model by a less accurate but computationally feasible one [12][13][14]. Let q " zptq and F be the accurate forward model given by (2.3).…”

Section: Bayesian Approximation Error Approachmentioning

confidence: 99%

“…Assume that e is separately independent of q and ζ. According to [13,14], the posterior distribution satisfies πpq|mq 9 πpm|qqπpqq " ż Y π e pm ´Fpqq ´ζqπpζ|qq dζ πpqq.…”

Section: Bayesian Approximation Error Approachmentioning

confidence: 99%

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A deterministic-statistical approach to reconstruct moving sources using sparse partial data

Liu,

Guo,

Sun

2021

Preprint

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We consider the reconstruction of moving sources using partial measured data. A twostep deterministic-statistical approach is proposed. In the first step, an approximate direct sampling method is developed to obtain the locations of the sources at different times. Such information is coded in the priors, which is critical for the success of the Bayesian method in the second step. The well-posedness of the posterior measure is analyzed in the sense of the Hellinger distance. Both steps are based on the same physical model and use the same set of measured data. The combined approach inherits the merits of the deterministic method and Bayesian inversion as demonstrated by the numerical examples.

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“…A modified Born iterative method (BIM) by which magnetic fields were analyzed and processed was investigated to retrieve more accurate images within the medical emergency time frame [9]. The Bayesian approximation error approach was used to partially recover the error structure induced by the Born approximation [10]. A new non-linear Born iterative reconstruction method with USguided depth-dependent 𝓁1 sparse regularization was proposed to improve diffuse optical tomography (DOT) reconstruction by incorporating a priori lesion depth and shape information from the co-registered US image [11].…”

Section: Introductionmentioning

confidence: 99%

A More Accurate Reconstruction Method for Detecting Large-Depth Defects in Plates Using SH Guided Waves

Wang

et al. 2020

Acta Mech. Solida Sin.

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The inspection of thickness thinning defects and corrosion defects is greatly significant for the health prediction of plate structures. The main aim of this research is to propose a novel and effective approach to achieve the accurate and rapid detection of arbitrary defects using shear horizontal (SH) guided waves, particularly for large-depth and complex defects. The proposed approach combines the quantitative detection of Fourier transform (QDFT) with a reference model-based strategy to improve the accuracy of large-depth defect detection. Since the shallow defect profile is theoretically constructed by inverse Fourier transform of the product of reflection coefficients and integral coefficients of reference models, the unknown large-depth defect can be initially assessed using the relevant information from a predefined reference model. By iteratively updating the integral coefficients of reference models, the accuracy of reconstruction of large-depth defects is much improved. To achieve the converged defect profile, a termination criterion, the root mean square error (RMSE), is applied to guarantee the construction of defects with a high level of accuracy. Moreover, the hybrid finite element method (HFEM) is used to simulate the propagation of SH guided waves in plates for calculating the reflection coefficients of plates with defects. Finally, to demonstrate the capability of the developed reconstruction method for defect detection in terms of accuracy and efficiency, three types of large-depth defect profiles, i.e., a rectangular flaw, a double-rectangular flaw, and a complex flaw, are examined. Results show that the discrepancy between the predicted defect profile and the real one is quite small, even in the largest-depth defect case where the defect depth is equal to 0.733 times the plate thickness, the minimal difference is observed. It is noted that the fast convergence of the proposed approach can be achieved by no more than ten updates for the worst case.

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A Bayesian approach to improving the Born approximation for inverse scattering with high-contrast materials

Cited by 15 publications

References 36 publications

Correlated Sample-Based Prior in Bayesian Inversion Framework for Microwave Tomography

Correlated Sample-Based Prior in Bayesian Inversion Framework for Microwave Tomography

A deterministic-statistical approach to reconstruct moving sources using sparse partial data

A More Accurate Reconstruction Method for Detecting Large-Depth Defects in Plates Using SH Guided Waves

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