Recovering multiscale buried anomalies in a two-layered medium

A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very easy and simple to implement. With the help of the factorization of the far field operator, we establish an inf-criterion for characterization of underlying scatterers. This result is then used to give a lower bound of the proposed indicator functional for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functional decays like the bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functional continuously dependents on the scattering amplitude, this further implies that the novel sampling method is extremely stable with respect to errors in the data. Different to the classical sampling method such as the linear sampling method or the factorization method, from the numerical point of view, the novel indicator takes its maximum near the boundary of the underlying target and decays like the bessel functions as the sampling points go away from the boundary. The numerical simulations also show that the proposed sampling method can deal with multiple multiscale case, even the different components are close to each other.

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“…We denote this subsequence again by {f j }. By Lemma 2.3(3), the difference operator T − T 0 is compact, which implies that 11) and thus also…”

Section: Assume That K 2 Is Not An Interior Transmission Eigenvaluementioning

confidence: 89%

A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency

Liu

2017

Inverse Problems

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106

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“…There is a large body of the literature on imaging methods for reconstructing geometric information about targets, such as their shapes, sizes and locations. We refer to, e.g., [2,3,8,9,11,18,[22][23][24]27] and references therein for well-known imaging techniques in inverse scattering such as level set methods, sampling methods, expansion methods, and shape optimization methods. However, for detecting or identifying, for instance, IEDs, the physical properties of the targets (in our model, the dielectric constants), would play a more important role [33].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm

Nguyen

Klibanov

Nguyen

et al. 2017

Journal of Computational Physics

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We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These data were collected using a microwave scattering facility at the University of North Carolina at Charlotte. The challenges for the inverse problem under the consideration are not only from its high nonlinearity and severe ill-posedness but also from the facts that the amount of the measured data is minimal and that these raw data are contaminated by a significant amount of noise, due to a non-ideal experimental setup. This setup is motivated by our target application in detecting and identifying explosives. We show in this paper how the raw data can be preprocessed and successfully inverted using our inversion method. More precisely, we are able to reconstruct the dielectric constants and the locations of the scattering objects with a good accuracy, without using any advanced a priori knowledge of their physical and geometrical properties.

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“…level set methods, sampling methods, expansion methods, shape optimization methods; see, e.g. [2,8,9,11,19,26,27] and references cited therein. The information about locations and shapes of targets is not sufficient to identify antipersonnel land mines and improvised explosive devices.…”

Section: Introductionmentioning

confidence: 99%

Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method

Nguyen

Klibanov

Nguyen

et al. 2017

Journal of Inverse and Ill-Posed Problems

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This paper is concerned with the numerical solution to a 3D coefficient inverse problem for buried objects with multi-frequency experimental data. The measured data, which are associated with a single direction of an incident plane wave, are backscatter data for targets buried in a sandbox. These raw scattering data were collected using a microwave scattering facility at the University of North Carolina at Charlotte. We develop a data preprocessing procedure and exploit a newly developed globally convergent inversion method for solving the inverse problem with these preprocessed data. It is shown that dielectric constants of the buried targets as well as their locations are reconstructed with a very good accuracy. We also prove a new analytical result which rigorously justifies an important step of the so-called "data propagation" procedure.

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Recovering multiscale buried anomalies in a two-layered medium

Cited by 48 publications

References 23 publications

A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency

A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency

Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm

Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method

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