A second degree Newton method for an inverse obstacle scattering problem

Kreß, Rainer; Lee, Kuo-Ming

doi:10.1016/j.jcp.2011.06.020

Cited by 6 publications

(9 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because of the compactness of the operators A ∞ and A ∞ , regularizations are necessary for both equations in (14). Summing up, for the second degree Newton's method, the following scheme is used:…”

Section: Second Degree Methodsmentioning

confidence: 99%

See 1 more Smart Citation

A second degree Newton method in inverse scattering problem for a crack

Lee

2012

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

Inverse scattering pre-stack depth imaging and it's comparison to some depth migration methods for imaging rich fault complex structure AIP Conf.For the inverse scattering problem from a sound-soft crack a second degree Newton method is proposed in this paper. Based on integral equations method, our scheme splits the inverse problem into a well-posed problem and a nonlinear ill-posed problem which will be linearized using a second degree method. Some reconstructions will be given to demonstrate the feasibility of the proposed method. C 2012 American Institute of Physics. [http://dx.

show abstract

Section: Second Degree Methodsmentioning

confidence: 99%

“…The first thing to note is that system (15) is the one which we actually solve, not system (14). System (14) is used to clarify the idea only.…”

Section: Second Degree Methodsmentioning

confidence: 99%

A second degree Newton method in inverse scattering problem for a crack

Lee

2012

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Quasi-Newton is less computational intensive than methods in the Newton-like family used in e.g. [47,44,46,42,16] and the references therein, while still offers good convergence rate of Newton's method cf. [47].…”

Section: Frequency-hopping Inversion Proceduresmentioning

confidence: 99%

Localization of small obstacles from back-scattered data at limited incident angles with full-waveform inversion

Barucq

Faucher

Pham

2018

Journal of Computational Physics

View full text Add to dashboard Cite

We investigate numerically the inverse problem of locating small circular obstacles in a homogeneous medium from multi-frequency back-scattered data limited to four angles of incidence. The main novelty of our paper is working with the position of the obstacles as parameter space in the frame work of full-waveform inversion (FWI) procedure. The computational cost of FWI is lowered by using a method based on single-layer potential. Reconstruction results are shown up to twenty-four obstacles, from initial guesses allowed to be far from the target. In experiments with six obstacles, we supplement the reconstruction with an analysis of the performance of the nonlinear conjugate gradient and quasi-Newton methods, in used with various line search algorithms.

show abstract

“…For a more stable and accurate solution of the inverse transmission problem we extend the approach suggested by Kress and Lee [18] that combines the ideas of Hettlich and Rundell [10] and Johansson and Sleeman [14] from the case of the inverse problem for an object that is perfect conductor to the case of the inverse problem for an object that penetrates the incident field.…”

Section: Thementioning

confidence: 99%

“…In the current paper, the third approach is carried out. In the spirit of [10], [14] and [18], given an approximation for the boundary in a first step the well-posed field equations can be solved for two densities on . Then in a second step, keeping the densities fixed, the ill-posed data equation can be linearised with respect to the boundary and we solve the linearised first degree data equation for a predictor.…”

Section: Thementioning

confidence: 99%

A second degree Newton method for an inverse scattering problem for a dielectric cylinder

Altundag¹

2015

Hittite J Sci Eng

View full text Add to dashboard Cite

fulfilling the transmission conditions I nverse scattering theory is concerned with methods for retrieving information on the geometry and the physical properties of obstacles from scattering of acoustic and electromagnetic wave. In the direct scattering problem the object is given and it is required to find the scattered wave. In the inverse scattering problem we want to receive information on geometry of the shape or physical parameters of the scattering object. The inverse obstacle scattering problem that we currently deal with is considered for time-harmonic waves. The scattering object is assumed to be a homogeneous scatterer and the inverse problem is to reconstruct an image of the scatterer. In this manuscript we are interested in dielectric obstacles and restrict ourselves to the sufficiently long cylinders. This

show abstract

A second degree Newton method for an inverse obstacle scattering problem

Cited by 6 publications

References 25 publications

A second degree Newton method in inverse scattering problem for a crack

A second degree Newton method in inverse scattering problem for a crack

Localization of small obstacles from back-scattered data at limited incident angles with full-waveform inversion

A second degree Newton method for an inverse scattering problem for a dielectric cylinder

Contact Info

Product

Resources

About