2009
DOI: 10.1007/s10444-009-9135-6
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Huygens’ principle and iterative methods in inverse obstacle scattering

Abstract: The inverse problem we consider in this paper is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the case of scattering from a sound-soft obstacle, we will interpret Huygens' principle as a system of two integral equations, named data and field equation, for the unknown boundary of the scatterer and the induced surface flux, i.e., the unknown normal derivative of the total field on the boundary. Reflecting the ill-posedness of th… Show more

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Cited by 48 publications
(36 citation statements)
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“…The Fréchet derivatives of any order still have the same mapping properties so that one can use the same numerical scheme for implementation of these new integral operators. Using these results, Ivanyshyn and Johansson applied this novel method for solving acoustic inverse obstacle scattering problems [25][26][27][28]. The algorithm has the significant advantage of avoiding the numerous numerical solution of boundary integral equations at each iteration step, that are replaced by matrix-vector products.…”
Section: Introductionmentioning
confidence: 99%
“…The Fréchet derivatives of any order still have the same mapping properties so that one can use the same numerical scheme for implementation of these new integral operators. Using these results, Ivanyshyn and Johansson applied this novel method for solving acoustic inverse obstacle scattering problems [25][26][27][28]. The algorithm has the significant advantage of avoiding the numerous numerical solution of boundary integral equations at each iteration step, that are replaced by matrix-vector products.…”
Section: Introductionmentioning
confidence: 99%
“…We note that regularization parameters α in (3.7), β for the equation system (3.14)-(3.17), γ for Eq. (3.15) and m in (4.2) are chosen by trial and error as a typical procedure which is applied in [23][24][25][26][27][28]. However, it is important to emphasize that the selection of the mentioned parameters do not affect the quality of the reconstructions if Table 1.…”
Section: Applications and Resultsmentioning
confidence: 99%
“…Density functions and related integral representations allow us to calculate the scattered and the total fields in each region. Then we employ iterative reconstruction algorithms introduced in [24,23] which were tested for shape reconstructions of objects in free-space [24][25][26] and for the ones buried in bounded domains [27,28].…”
Section: Introductionmentioning
confidence: 99%
“…The interrelation between simultaneous linearization method and the traditional Newton method was established in the paper published by Ivanyshyn, Kress, and Serranho [18] for impenetrable scatterer. In the following theorem we state an interrelation between these two iterative method for penetrable scatterer.…”
Section: Iterative Scheme For the Simultaneous Linearization Methodsmentioning
confidence: 99%