Through-the-Wall Nonlinear SAR Imaging

Klibanov, Michael V.; Smirnov, Alexey V.; Khoa, Vo Anh; Sullivan, Anders; Nguyen, Lam

doi:10.1109/tgrs.2021.3055805

Cited by 15 publications

(10 citation statements)

References 25 publications

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“…However, in Section 7, we explain how to approximate the missing function g 1 . The schematic diagram of the data collection is displayed on Figure 1.We have also discovered recently that Problem 1.1 plays the key role in the nonlinear synthetic-aperture radar (SAR) imaging, including SAR experimental data [32,22].…”

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confidence: 99%

“…Hence, the methods based on Born approximation or/and Born series work for the case when the size of the target is small and the contrast c target /c bckgr 1 where c target is the dielectric constant of the target and c bckgr is the dielectric constant of the background (or the environment around the target). For example, it was demonstrated numerically on [32] that the Born approximation is not capable to deliver accurate values of dielectric constants of targets for SAR-like data in the case of high target/background contrasts.…”

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confidence: 99%

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Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data

Klibanov¹,

Le²,

Nguyen³

et al. 2022

IPI

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<p style='text-indent:20px;'>To compute the spatially distributed dielectric constant from the backscattering computationally simulated ane experimentally collected data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve this inverse problem, we establish a new version of the Carleman estimate and then employ this estimate to construct a cost functional, which is strictly convex on a convex bounded set of an arbitrary diameter in a Hilbert space. The strict convexity property is rigorously proved. This result is called the convexification theorem and it is the central analytical result of this paper. Minimizing this cost functional by the gradient descent method, we obtain the desired numerical solution to the coefficient inverse problems. We prove that the gradient descent method generates a sequence converging to the minimizer starting from an arbitrary point of that bounded set. We also establish a theorem confirming that the minimizer converges to the true solution as the noise in the measured data and the regularization parameter tend to zero. Unlike the methods, which are based on the optimization, our convexification method converges globally in the sense that it delivers a good approximation of the exact solution without requiring a good initial guess. Results of numerical studies of both computationally simulated and experimentally collected data are presented.</p>

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confidence: 99%

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confidence: 99%

Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data

Klibanov¹,

Le²,

Nguyen³

et al. 2022

IPI

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“…The start for numerical studies of the convexification was given in the paper [1]. Thus, in follow up publications [24,25,30,16,14,15,24,25,27,28,29,32,33,30,40,50,51] the theoritical results for the convexification are combined with the numerical ones. In particular, some of these papers work with experimentally collected backscattering data [14,15,26,32,33].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, in follow up publications [24,25,30,16,14,15,24,25,27,28,29,32,33,30,40,50,51] the theoritical results for the convexification are combined with the numerical ones. In particular, some of these papers work with experimentally collected backscattering data [14,15,26,32,33]. We also refer to the recently published book of Klibanov and Li [31], in which many of these results are described.…”

Section: Introductionmentioning

confidence: 99%

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Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data

Le,

Klibanov,

Nguyen

et al. 2021

Preprint

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It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the corresponding numerical method is established. Numerical studies for both computationally simulated and experimentally collected data are presented. The experimental part is concerned with the problem of computing dielectric constants of explosive-like targets in the standoff mode using severely underdetermined data.

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Numerical solution of the 3-D travel time tomography problem

Klibanov

Zhang

2023

Journal of Computational Physics

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Through-the-Wall Nonlinear SAR Imaging

Cited by 15 publications

References 25 publications

Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data

Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data

Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data

Numerical solution of the 3-D travel time tomography problem

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