Inverse acoustic scattering problem in half-space with anisotropic random impedance

Helin, Tapio; Lassas, Matti; Päivärinta, Lassi

doi:10.1016/j.jde.2016.11.006

Cited by 19 publications

(17 citation statements)

References 27 publications

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“…Our paper provides continuation to previous work by the authors in [32,25,9], where the averaging procedure to estimate correlations is based on a single realization of the observed data, i.e., the random potential or boundary condition is sampled only once. Such an approach can reveal valuable information of the leading order statistics of the unknown field.…”

Section: Previous Literaturementioning

confidence: 68%

Correlation imaging in inverse scattering is tomography on probability distributions

et al. 2018

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Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be recovered from correlations between amplitude measurements of the leading singularities, detected in the exterior of a region where the potential is almost surely supported. The result is then applied to show that if two sufficiently regular random fields yield the same data, they have identical laws as function-valued random variables.

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Section: Previous Literaturementioning

confidence: 68%

Correlation imaging in inverse scattering is tomography on probability distributions

et al. 2018

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“…In this regard our paper provides the first study of random source problems in fractional diffusion models. Let us also point out that correlation based imaging has been considered for problems where the randomness is an inherent property of the medium or boundary condition [21,22,10,17,23,16,15,8].…”

Section: Previous Literaturementioning

confidence: 99%

An inverse random source problem in a stochastic fractional diffusion equation

2020

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In this work the authors consider an inverse source problem in the following stochastic fractional diffusion equationThe interested inverse problem is to reconstruct f (x) and g(x) by the statistics of the final time data u(x, T ). Some direct problem results are proved at first, such as the existence, uniqueness, representation and regularity of the solution. Then the reconstruction scheme for f and g is given. To tackle the ill-posedness, the Tikhonov regularization is adopted. Finally we give a regularized reconstruction algorithm and some numerical results are displayed.

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“…We also mention the closely related topic of imaging random media by time reversal techniques [2,9,10,17] as well as inverse scattering from random potential or random boundary conditions [11,25,39].…”

Section: 2mentioning

confidence: 99%

“…Thus for every f ∈ N (B) we are able to find w f . In particular, in the inner products (25) w f , κ 2 w h L 2 ((0,∞)×X ) , f ∈ N (B), the left factor w f is known. Observe that for any φ ∈ C ∞ 0 (B) we have w f = φ where f = g φ ∈ N (B), and therefore the inclusion…”

Section: Reduction To the Deterministic Inverse Problemmentioning

confidence: 99%

Correlation based passive imaging with a white noise source

Helin

Lassas

Oksanen

et al. 2018

Journal de Mathématiques Pures et Appliquées

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Passive imaging refers to problems where waves generated by unknown sources are recorded and used to image the medium through which they travel. The sources are typically modelled as a random variable and it is assumed that some statistical information is available. In this paper we study the stochastic wave equation ∂ 2 t u − ∆ g u = χW , where W is a random variable with the white noise statistics on R 1+n , n ≥ 3, χ is a smooth function vanishing for negative times and outside a compact set in space, and ∆ g is the Laplace-Beltrami operator associated to a smooth non-trapping Riemannian metric tensor g on R n . The metric tensor g models the medium to be imaged, and we assume that it coincides with the Euclidean metric outside a compact set. We consider the empirical correlations on an open set X ⊂ R n ,for T > 0. Supposing that χ is non-zero on X and constant in time after t > 1, we show that in the limit T → ∞, the data C T becomes statistically stable, that is, independent of the realization of W . Our main result is that, with probability one, this limit determines the Riemannian manifold (R n , g) up to an isometry. To our knowledge, this is the first result showing that a medium can be determined in a passive imaging setting, without assuming a separation of scales.Date: May 7, 2019.

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Inverse acoustic scattering problem in half-space with anisotropic random impedance

Cited by 19 publications

References 27 publications

Correlation imaging in inverse scattering is tomography on probability distributions

Correlation imaging in inverse scattering is tomography on probability distributions

An inverse random source problem in a stochastic fractional diffusion equation

Correlation based passive imaging with a white noise source

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