Adaptive eigenspace for multi-parameter inverse scattering problems

Grote, Marcus J.; Nahum, Uri

doi:10.1016/j.camwa.2019.02.005

Cited by 12 publications

(26 citation statements)

References 28 publications

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“…We consider two additional experiments, which are derived from Experiments 1 and 2 of Table 8, with one major difference: the set of eigenvectors is recomputed from the current iteration model every 30 iterations. This is advocated in De Buhan & Kray (2013); Grote & Nahum (2019) where, contrary to our experiments, the background velocity is mostly known.…”

Section: A Two-dimensional Reconstruction With Evolution Of Basismentioning

confidence: 60%

“…For the decomposition of images with layered patterns, only a few formulations perform well (η 1 , η 3 , η 6 ). It would be interesting to investigate further the performance of anisotropic or directional diffusion coefficients, mentioned by Weickert (1998); Grote & Nahum (2019).…”

Section: Resultsmentioning

confidence: 99%

“…In our work, we employ the regularization by discretization approach: instead of adding the regularization term I in the minimization problem, we remain with Problem (5), and use a specific representation for the model (unknown). We follow the work of De Buhan & Osses (2010); De Buhan & Kray (2013); Grote et al (2017); Grote & Nahum (2019) with the "Adaptive Inversion" or "Adaptive Eigenspace Inversion" method. Namely, the unknown is represented via a decomposition into the basis of eigenvectors computed from a diffusion PDE.…”

Section: Eigenvector Model Decomposition In Fwimentioning

confidence: 99%

“…In our work, we will use a model decomposition based upon the eigenvectors of a chosen diffusion operator, as introduced by De Buhan & Kray (2013); Grote et al (2017); Grote & Nahum (2019). Note that this decomposition is shown (with the right choice of operator) to be related with the more standard Total Variation (TV) or Tikhonov regularizations.…”

Section: Introductionmentioning

confidence: 99%

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Eigenvector models for solving the seismic inverse problem for the Helmholtz equation

Faucher

Scherzer

Barucq³

2020

Geophysical Journal International

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We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter is represented using a limited number of coefficients associated with a basis of eigenvectors of a diffusion equation, following the regularization by discretization approach. We compare several choices for the diffusion coefficient in the partial differential equations, which are extracted from the field of image processing. We first investigate their efficiency for image decomposition (accuracy of the representation with respect to the number of variables and denoising). Next, we implement the method in the quantitative reconstruction procedure for seismic imaging, following the Full Waveform Inversion method, where the difficulty resides in that the basis is defined from an initial model where none of the actual structures is known. In particular, we demonstrate that the method is efficient for the challenging reconstruction of media with salt-domes. We employ the method in two and three-dimensional experiments, and show that the eigenvector representation compensates for the lack of low-frequency information, it eventually serves us to extract guidelines for the implementation of the method.

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Section: A Two-dimensional Reconstruction With Evolution Of Basismentioning

confidence: 60%

Section: Resultsmentioning

confidence: 99%

Section: Eigenvector Model Decomposition In Fwimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Eigenvector models for solving the seismic inverse problem for the Helmholtz equation

Faucher

Scherzer

Barucq³

2020

Geophysical Journal International

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“…Once all the needed information is available on a small neighborhood of D S , enclosing the unknown scatterer O, we perform the recovery by solving an inverse problem. Here, we opt for the Adaptive Eigenspace method [14,13,22,25], which enables the inversion with only a few parameters.…”

Section: A Three-step Strategymentioning

confidence: 99%

How to solve inverse scattering problems without knowing the source term: a three-step strategy

Graff¹,

Grote²,

Nataf³

et al. 2019

Inverse Problems

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The solution of inverse scattering problems always presupposed knowledge of the incident wavefield and require repeated computations of the forward problem, for which knowing the source term is crucial. Here we present a three-step strategy to solve inverse scattering problems when the time signature of the source is unknown. The proposed strategy combines three recent techniques: (i) wave splitting to retrieve the incident and the scattered wavefields, (ii) time-reversed absorbing conditions (TRAC) for redatuming the data inside the computational domain, (iii) adaptive eigenspace inversion (AEI) to solve the inverse problem. Numerical results illustrate step-by-step the feasibility of the proposed strategy. * Earlier known as Marie Kray.

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An adaptive eigenfunction basis strategy to reduce design dimension in topology optimization

Sanders

Bonnet

Aquino

2021

Numerical Meth Engineering

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Adaptive eigenspace for multi-parameter inverse scattering problems

Cited by 12 publications

References 28 publications

Eigenvector models for solving the seismic inverse problem for the Helmholtz equation

Eigenvector models for solving the seismic inverse problem for the Helmholtz equation

How to solve inverse scattering problems without knowing the source term: a three-step strategy

An adaptive eigenfunction basis strategy to reduce design dimension in topology optimization

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