Some Quasi-Analytic and Numerical Methods for Acoustical Imaging of Complex Media

Wirgin, Armand

doi:10.1007/978-3-7091-2486-4_5

Cited by 10 publications

(27 citation statements)

References 43 publications

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“…Ideally, one should choose to employ the best possible (exact) theoretical model in conjunction with error-free data, but this is usually neither possible (all measurements, except those one might want to simulate, are error-ridden) nor desirable (using fullblown theoretical models involves a very heavy computational load that is often in *E-mail: wirgin@lma.cnrs-mrs.fr conflict with real-time inversion requirements and/or there are many situations in which one can be satisfied with less-than-perfect reconstructions [5]). …”

Section: Introductionmentioning

confidence: 98%

“…However, there exists a class of problems (e.g. [5]) in which the inversion of the N p parameters reduces to N p problems involving the inversion of only a single parameter (e.g., finding the shape of a body by employing scattered field data and a simplified model, such as the physical optics approximation, of the wave/body interaction). In the following, attention will be focused on such a class of inverse problems, and, in particular, on one of its members (which should reveal the features of the other members of the class).…”

Section: Introductionmentioning

confidence: 99%

“…The solution of the forward problem is well known by virtue of the Fresnel formulae [5]. The corresponding inverse problem is that of the recovery of the single parameter constituted by the real index of refraction of the medium occupying one of the half spaces from data (a single piece should be sufficient) pertaining to the reflection coefficient.…”

Section: Introductionmentioning

confidence: 99%

“…, d M g. The measurement process induces errors in the data that are partly uncontrollable and/or unpredictable and the chosen theoretical model is usually not exact (i.e., does not account for all of the properties of the physical configuration and of the interaction of the probe field with this configuration). This has repercussions on the fundamental ill-posedness [1][2][3][4][5] (i.e., the non-existence, and/or the non-uniqueness and/or the instability of solutions with respect to small variations in the data and/ or the model) of the inverse problem and on the accuracy of the reconstruction of p.…”

Section: Introductionmentioning

confidence: 99%

“…Solving inverse problems [1][2][3][4][5] for a N p -dimensional vector p of parameters p 1 , p 2 , . .…”

Section: Introductionmentioning

confidence: 99%

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Ill-Posedness and Accuracy in Connection with the Recovery of a Single Parameter from a Single Measurement

Wirgin

2002

Inverse Problems in Engineering

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A particular one-parameter problem, that of the reflection and refraction of a plane wave at a planar boundary between two media, which can be solved in closed form in both the direct and inverse contexts, is chosen to illustrate the ill-posed nature of a class of more general inverse problems and to show how the quality of the reconstruction of the parameter varies with the accuracy of the data on the one hand, and the accuracy of the interaction model employed in the inversion scheme on the other hand.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Solving inverse problems [1][2][3][4][5] for a N p -dimensional vector p of parameters p 1 , p 2 , . .…”

Section: Introductionmentioning

confidence: 99%

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Ill-Posedness and Accuracy in Connection with the Recovery of a Single Parameter from a Single Measurement

Wirgin

2002

Inverse Problems in Engineering

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Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

Groby

Ryck

Leclaire

et al. 2006

Math Methods in App Sciences

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A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative to slab-like macroscopically inhomogeneous porous obstacles. It is shown how to numerically solve such problems, involving both spatially-varying density and compressibility, by means of an iterative scheme initialized with a Born approximation. A numerical solution is obtained for a canonical problem involving a two-layer slab. IntroductionThis work was initially motivated by two problems: i) the design problem connected with the determination of the optimal profile of a continuous and/or discontinuous spatial distribution of the material/geometric properties of porous materials for the absorption of sound [7] and ii) the retrieval of the spatially-varying mechanical and geometrical parameters of bone for the diagnosis of diseases such as osteoporosis [10].Such inverse problems [20] can be decomposed into two sub-problems: i) the determination of the constitutive and conservation relations linking the various spatially-variable mechanical parameters of the porous medium to its response to an acoustic solicitation, and ii) the resolution of the * Correspondence to: J.-P. Groby, Akoestieke en Thermische Fysica, KULeuven, Celestijnenlaan 200D , 3001 Heverlee, Belgium † E-mail: jeanphilippe.groby@fys.kuleuven.be 1 wave equation in an inhomogeneous porous medium (for instance, within the Biot, or rigid frame approximations). Here we focus on the second point.In [17], it is shown that the wave equation describing the propagation in a macroscopicallyinhomogeneous porous medium in the rigid frame approximation can formally take the form of the usual acoustic wave equation in a macroscopically-inhomogeneous fluid (in which the microscopic features of the porous medium are homogenized) with spatial (and frequency) dependent compressibility κ e (x, ω) and density ρ e (x, ω).The present work deals with a method of resolution of direct problems involving acoustic wave propagation in a macroscopically-inhomogeneous fluid medium, whose density and compressibility are both space dependent, this being a prerequisite to the resolution of related inverse problems.This topic is also of great interest in quantum physics (inverse potential scattering [2,37,38,39]), ocean acoustics [9,8,32,11,36,12] (detection of inhomogeneities, sediment exploration, influence of seawater and seafloor composition and heterogenity on the long-range propagation of acoustic waves in the sea, ...), seismology [1,40,42] (determination of the internal structure and composition of the Earth via seismic waves,...), geophysics [42,25,48,44] (characterization of soil, detection of geological features such as hydrocarbon reservoirs, ...), optics and electromagnetism [47,41] (design and characterization of materials having specified response to waves, detection of flaws,...).The wave equation in an inhomogeneous medi...

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Multiparameter identification of a lossy fluid-like object from its transient acoustic response

Scotti

Wirgin

2013

Inverse Problems in Science and Engineering

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International audienceA transient acoustic wave multiparameter inverse problem is studied. The aim is to simultaneously retrieve three constitutive parameters and one geometrical parameter of a lossy fluid-like cylinder by nonlinear full-wave inversion of synthetic data. Contrary to most publications treating this subject, it is assumed herein that the retrieval model is not identical to the data model, this being so because some of the parameters (priors) in the retrieval model are different (by the simple fact of being more or less unknown) from their true counterparts in the data model. This so-called model discordance, which is the usual situation in real-world inverse problems, is a source of errors for the retrieval of the other parameters. Moreover, it is a source of non-uniqueness and instability, a fact revealed by the employment of a properly-tuned Nelder-Mead downhill Simplex optimization algorithm, and which requires a second-order regularization for its resolution. Retrieval errors as a function of prior uncertainty are computed, and found to be large, for various model discordance scenarios involving one or two uncertain priors, for data with and without noise

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Some Quasi-Analytic and Numerical Methods for Acoustical Imaging of Complex Media

Cited by 10 publications

References 43 publications

Ill-Posedness and Accuracy in Connection with the Recovery of a Single Parameter from a Single Measurement

Ill-Posedness and Accuracy in Connection with the Recovery of a Single Parameter from a Single Measurement

Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves

Multiparameter identification of a lossy fluid-like object from its transient acoustic response

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