Second-harmonic imaging in random media

Borcea, Liliana; Li, Wei; Mamonov, A.; Schotland, John C.

doi:10.1088/1361-6420/aa6ab1

Cited by 4 publications

(5 citation statements)

References 39 publications

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“…The first inverse problem is therefore to reconstruct (Γ, σ, η) from the data H (2) in (12) with the model for u (1) and v (1) given in (9). By taking h 1 = 0, the problem reduces to reconstructing (Γ, σ, η) from the data H (2) = 2Γσu (1) * u (1) , (14) with the model for u (1) given in (9). When Γ and η are known, this problem was analyzed in [6,11].…”

Section: The Reconstruction Of (γ σ η)mentioning

confidence: 99%

“…where ∆ denotes the standard Laplacian operator, and u * denotes the complex conjugate of u. This system serves as a simplified model of the second harmonic generation process in a heterogeneous medium excited by an incident wave source g [14,15,17,23,35,37,38]. The fields u and v are, respectively, the incident field (with wave number k) and the generated secondharmonics (with wave number 2k).…”

Section: Introductionmentioning

confidence: 99%

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Recovering coefficients in a system of semilinear Helmholtz equations from internal data

Ren,

Soedjak

2024

Inverse Problems

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We study an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients in the system from internal data measured in applications such as thermoacoustic imaging. We derive results on the uniqueness and stability of the inverse problem in the case of small boundary data based on the technique of first- and higher-order linearization. Numerical simulations are provided to illustrate the quality of reconstructions that can be expected from noisy data.

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Section: The Reconstruction Of (γ σ η)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Recovering coefficients in a system of semilinear Helmholtz equations from internal data

Ren,

Soedjak

2024

Inverse Problems

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“…If the background heterogeneity is characterized by rapid variations and is known only statistically, identification may still be successful owing to the tools of TR in random media; see, e.g., Refs. 37–42. On the other hand, identification of a small cavity in a geophysical medium with a high degree of homogeneity, using TR, would be difficult, since the amount of information recorded in the sensors would typically be small.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…See, e.g., Refs. 37–42. A simple explanation for the success of TR in a “deterministic” bounded domain can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

Scatterer identification in a 2D geophysical medium using an augmented computational time reversal method

Rabinovich

Givoli

Bielak³

et al. 2021

Num Anal Meth Geomechanics

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The problem of identifying an obstacle (scatterer) in the form of a cavity in a 2D geophysical medium is considered. This is posed as an inverse wave problem, where the location of the cavity is sought based on measurements of the elastic waves recorded by sensors located at certain points in the domain. The sensor measurements are noisy, and are generated synthetically as a first step. The inverse problem is solved by seeking the minimum of a specially designed cost functional, based on a computational time reversal (TR) procedure, where waves are radiated back in time from the sensors. The cost functional is defined to measure, for each scatterer candidate in the search space, the quality of the refocusing of the backward‐propagating waves on the given wave source at the end of the TR process. While the basic idea has appeared in previous publications, here it is applied to a 2D heterogeneous geophysical model (albeit a relatively simple one), and is enhanced by using several auxiliary techniques. These include (a) an “augmentation” technique, which is used to strengthen the coherent information (and thus to weaken the noncoherent information) by solving an elliptic problem at each time step; (b) experimentation with both instantaneous (impact) sources and time‐harmonic sources of finite duration; (c) combining the identification results of several sources and several source wavelengths to enhance identification; (d) reducing the size of the search space by a special “zooming in” technique; and (e) defining a performance index to assess the method's success and to provide a measure of confidence in the identification result in each specific case. Several numerical experiments are presented that demonstrate the performance of the proposed schemes. The sensitivity of the identification process to various parameters of the scatterer, the measurements, and the medium is investigated.

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“…In this paper, we consider the inverse obstacle scattering problem with an emphasis on resolution enhancement. Motivated by nonlinear optics [10,11,38], we utilize nonlinear point scatterers to excite high harmonic generation so that enhanced resolution can be achieved to reconstruct the obstacles. To realize this idea, we have to consider the scattering problem of a time-harmonic plane incident wave by a heterogeneous medium, which consists of small scale point scatterers and wavelength comparable extended obstacles.…”

Section: Introductionmentioning

confidence: 99%

A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterers

Lai¹,

Li²,

Li³

et al. 2018

Inverse Problems &Amp; Imaging

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Consider the scattering of a time-harmonic plane wave by heterogeneous media consisting of linear or nonlinear point scatterers and extended obstacles. A generalized Foldy-Lax formulation is developed to take fully into account of the multiple scattering by the complex media. A new imaging function is proposed and an FFT-based direct imaging method is developed for the inverse obstacle scattering problem, which is to reconstruct the shape of the extended obstacles. The novel idea is to utilize the nonlinear point scatterers to excite high harmonic generation so that enhanced imaging resolution can be achieved. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.2010 Mathematics Subject Classification. 78A46, 78M15, 65N21.

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Second-harmonic imaging in random media

Cited by 4 publications

References 39 publications

Recovering coefficients in a system of semilinear Helmholtz equations from internal data

Recovering coefficients in a system of semilinear Helmholtz equations from internal data

Scatterer identification in a 2D geophysical medium using an augmented computational time reversal method

A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterers

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