Point Sources and Multipoles in Inverse Scattering Theory

Potthast, Roland

doi:10.1201/9781420035483

Cited by 248 publications

(309 citation statements)

References 38 publications

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“…These methods are motivated by the uniqueness proof of inverse scattering problems and are based on the fact that the point source incident wave becomes singular as the source approaches to the boundary of scatterers (see Colton and Kress [11]). We refer to Potthast [20] and Kirsch and Grinberg [16] for more information on this class of methods.…”

Section: Introductionmentioning

confidence: 99%

Reverse time migration for extended obstacles: acoustic waves

Chen

Huang

2013

Inverse Problems

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Abstract. We consider the resolution of the single frequency reverse time migration (RTM) method for extended targets without the assumption of the validation of geometric optics approximation. The resolution analysis, which applies in both penetrable and non-penetrable obstacles with sound soft or impedance boundary condition on the boundary of the obstacle, implies that the imaginary part of the crosscorrelation imaging functional is always positive and thus may have better stability properties. Numerical experiments are included to illustrate the powerful imaging quality and to confirm our resolution results.

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Section: Introductionmentioning

confidence: 99%

Reverse time migration for extended obstacles: acoustic waves

Chen

Huang

2013

Inverse Problems

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“…The linear sampling method [7], the factorization method [16] and the singular sources method [21] construct the indicator functions from the far-field pattern directly, while the probe method [13,14] constructs the indicator in terms of the near field. The near field can be obtained from the far field by some regularization procedures [21]. However, we can also state the natural version of the probe method directly from the far field data, without reducing the far field to the near field, see [11].…”

Section: Introduction and Examplesmentioning

confidence: 99%

Reconstruction of the Shape and Surface Impedance from Acoustic Scattering Data for an Arbitrary Cylinder

Liu¹,

Nakamura²,

Sini³

2007

SIAM J. Appl. Math.

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Abstract. The inverse scattering for an obstacle D ⊂ R 2 with mixed boundary condition can be considered as a prototype for radar detection of complex obstacles with coated and non-coated parts of the boundary. We construct some indicator functions for this inverse problem using the far-field pattern directly, without the necessity to transform the far-field to the near field. Based on the careful singularity analysis, these indicator functions enable us to reconstruct the shape of the obstacle and distinguish the coated from the non-coated part of the boundary. Moreover, an explicit representation formula for the surface impedance in the coated part of the boundary is also given. Our reconstruction scheme reveals that the coated part of the obstacle is less visible than the non-coated one, which corresponds to the physical fact that the coated boundary absorbs some part of the scattered wave. Numerics are presented for the reconstruction formulas, which show that both the boundary shape and the surface impedance in the coated part of boundary can be reconstructed accurately. The theoretical reconstruction techniques proposed in this work can be applied in the practical 3-dimensional electromagnetic inverse scattering problems with hopeful numerical performances, which are of great importance in the design of non-detectable obstacles.

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“…On the other hand, point-source near-field inverse scattering problems for a small soft or hard sphere were studied in (8). For other implementations of near-field inverse problems see (9), and p. 133 of (10); also we point out the point-source inverse scattering methods analyzed in (11). In all the above investigations the incident wave is generated by a point-source located in the exterior of the scatterer.…”

Section: Introductionmentioning

confidence: 99%

Inverse Scattering in the Low-Frequency Region by Using Acoustic Point Sources

Tsitsas¹

2011

Waves in Fluids and Solids

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Point Sources and Multipoles in Inverse Scattering Theory

Cited by 248 publications

References 38 publications

Reverse time migration for extended obstacles: acoustic waves

Reverse time migration for extended obstacles: acoustic waves

Reconstruction of the Shape and Surface Impedance from Acoustic Scattering Data for an Arbitrary Cylinder

Inverse Scattering in the Low-Frequency Region by Using Acoustic Point Sources

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