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In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here, we propose and analyze new direct sampling methods for this problem. The first method we consider uses a far-field transformation of the near-field data, which allows us to derive explicit bounds in the resolution analysis for the direct sampling method’s imaging functional. Two direct sampling methods are studied, using the far-field transformation. For these imaging functionals, we use the Funk–Hecke identities to study the resolution analysis. We also study a direct sampling method for the case of the given Cauchy data. Numerical examples are given to show the applicability of the new imaging functionals for recovering a sound soft scatterer with full and partial aperture data.
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Direct sampling for recovering a clamped cavity from the biharmonic far-field data
Abstract This paper concerns the inverse shape problem of recovering an unknown clamped cavity embedded in a thin infinite plate. The model problem is assumed to be governed by the two-dimensional biharmonic wave equation in the frequency domain. Based on the far-field data, a resolution analysis is conducted for cavity recovery via the direct sampling method. The Funk–Hecke integral identity is employed to analyze the performance of two imaging functions. Our analysis demonstrates that the same imaging functions commonly used for acoustic inverse shape problems are applicable to the biharmonic wave context. This work presents the first extension of direct sampling methods to biharmonic waves using far-field data. Numerical examples are provided to illustrate the effectiveness of these imaging functions in recovering a clamped cavity.
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- Award ID(s):
- 2208256
- PAR ID:
- 10574459
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Inverse Problems
- Volume:
- 41
- Issue:
- 3
- ISSN:
- 0266-5611
- Format(s):
- Medium: X Size: Article No. 035013
- Size(s):
- Article No. 035013
- Sponsoring Org:
- National Science Foundation
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