Eigenvector Model Descriptors for Solving an Inverse Problem of Helmholtz Equation

Abstract : We study the inverse problem for the Helmholtz equation using partial data from one-side illumination. In order to reduce the ill-posedness of the problem, the model to be recovered is represented using a limited number of coefficients associated with a basis of eigenvectors, following regularization by discretization approach. The eigenvectors result from a diffusion equation and we compare several choices of weighting coefficient from image processing theory. We first investigate their efficiency for image decomposition (accuracy of the representation with a small number of variables, denoising). Depending on the model geometry, we also highlight potential difficulties in the choice of basis and underlying parameters. Then, we implement the method in the context of iterative reconstruction procedure, following a seismic setup. Here, the basis is defined from an initial model where none of the actual structures are known, thus complicating the process. We note that the method is more appropriate in case of salt dome media (which remains a very challenging situation in seismic), where it can compensate for lack of low frequency information. We carry out two and three-dimensional experiments of reconstruction to illustrate the influence of the basis selection, and give some guidelines for applications.
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Contributor : Florian Faucher <>
Submitted on : Friday, March 22, 2019 - 8:50:25 AM
Last modification on : Friday, April 12, 2019 - 10:46:02 AM

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  • HAL Id : hal-02076210, version 1
  • ARXIV : 1903.08991


Hélène Barucq, Florian Faucher, Otmar Scherzer. Eigenvector Model Descriptors for Solving an Inverse Problem of Helmholtz Equation. 2019. ⟨hal-02076210⟩



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