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Level set methods for inverse scattering

Dorn, Oliver ; Lesselier, Dominique

Inverse Problems, 2006, Vol.22(4), pp.R67-R131 [Tạp chí có phản biện]

ISSN: 0266-5611 ; E-ISSN: 1361-6420 ; DOI: 10.1088/0266-5611/22/4/R01

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  • Nhan đề:
    Level set methods for inverse scattering
  • Tác giả: Dorn, Oliver ; Lesselier, Dominique
  • Chủ đề: Mathematics/Mathematical Physics ; Engineering Sciences/Electromagnetism ; Engineering Sciences/Acoustics ; Physics/Mechanics/Acoustics ; Engineering Sciences/Optics / Photonic ; Mathematics/Optimization And Control ; Inverse Scattering ; Imaging ; Level-Set ; Evolution Of Shapes ; Shape Sensitivity Analysis ; Topological Derivative
  • Là 1 phần của: Inverse Problems, 2006, Vol.22(4), pp.R67-R131
  • Mô tả: We give an overview of recent techniques which use a level set representation of shapes for solving inverse scattering problems. The main focus is on electromagnetic scattering using different popular models, such as for example Maxwell's equations, TM-polarized and TE-polarized waves, impedance tomography, a transport equation or its diffusion approximation. These models are also representative of a broader class of inverse problems. Starting out from the original binary approach of Santosa for solving the corresponding shape reconstruction problem, we successively develop more recent generalizations, such as for example using colour or vector level sets. Shape sensitivity analysis and topological derivatives are discussed as well in this framework. Moreover, various techniques for incorporating regularization into the shape inverse problem using level sets are demonstrated, which also include the choice of subclasses of simple shapes, such as ellipsoids, for the inversion. Finally, we present various numerical examples in two dimensions and in three dimensions for demonstrating the performance of level set techniques in realistic applications.
  • Ngôn ngữ: English
  • Số nhận dạng: ISSN: 0266-5611 ; E-ISSN: 1361-6420 ; DOI: 10.1088/0266-5611/22/4/R01

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