Recent Developments in Inverse Acoustic Scattering Theory

By David Colton, J. Coyle, Peter B. Monk. SIAM Review, 2000

367 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Mathematical Physics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/93300e991bab8b4c04db766a86473cae0f747260

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Citations in the corpus

The linear sampling method for cracks (2003, methodology): “In particular, we propose to use the linear sampling method [5] to arrive at the solution of this inverse scattering problem and difficulties arise from the fact that the crack has an empty interior.”
The scattering support (2003, methodology): “Finally, we mention that the ideas we will discuss below are motivated by the Linear Sampling Method of Colton- Kirsch [ 2 ], and the subsequent factorization of the far field operator by Kirsch [6].”
A high-order algorithm for obstacle scattering in three dimensions (2004, background): “Computation of the far field pattern plays an important role in inverse scattering theory, to identify the shape of the scatterers, such as buried objects [8, 9] .”
Inverse scattering problems with multi-frequencies (2015, background): “Due to lack of stability, the inverse scattering problems are severely ill-posed at a fixed frequency [70].”
AN APPROXIMATION PROPERTY OF IMPORTANCE IN INVERSE SCATTERING THEORY (2001, methodology): “Introduction This paper is devoted to the problem of deriving an approximation theorem for the Helmholtz equation which is of central importance in the linear sampling method for solving the inverse scattering problem for time-harmonic acoustic waves [5].”
Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking (2013, background): “The asymptotic theory nicely reproduces this asymptotically with f giving the decay envelope, further details can be found in [8] where other topical issues such as ultra-refraction and all-angle negative refraction are also covered.”
A survey on sampling and probe methods for inverse problems (2006, methodology): “In 2000, the development status of the method has been summarized in the survey article [18] by Colton, Coyle and Monk.”
Contrast Source Inversion Method: State of Art (2001, background): “[8], and Sabatier [26] and Van den Berg [29].”
A survey of finite element methods for time-harmonic acoustics (2006, background): “Recent techniques, such as the linear sampling method [7], avoid repeated solution of direct problems, yet involve smaller-scale optimization problems by requiring measurements for a large number of incident waves.”
The inverse electromagnetic scattering problem for anisotropic media (2010, methodology): “In the following numerical study, we approximate us and uint using a cubic finite element method with a perfectly matched layer, and hence can evaluate an approximation to u∞ which is then modified by adding random noise as in [9].”
On the Mathematical Basis of the Linear Sampling Method (2003, methodology): “subject of considerable attention since its introduction [ 2 ], [10]-[12].”
The linear sampling method in inverse electromagnetic scattering theory (2003, methodology): “Applications of the linear sampling method to practical problems have been considered in microwave tomography, in the case of the detection of leukaemia in human bone marrow [19], in impedance tomography [3], in elasticity [1, 12, 23, 47] and for the detection of buried objects [ 14 ].”
Recent progress in electrical impedance tomography (2003, methodology): “In this paper, Kirsch put earlier investigations by Colton and himself [12] (the so-called linear sampling method, see also the survey by Colton et al [11]) in a proper context and developed what is now called the factorization method in inverse scattering.”