Inversion of Microwave Scattering Patterns

Fedotowsky, A.; Boivin, Germain; Tremblay, R.

doi:10.1139/p71-368

Cited by 6 publications

(6 citation statements)

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“…Other authors have considered the linear versions of several inverse problems involving the wave equation [30,31]. They use the well known Born approximation to linearise their problems.…”

Section: The Linearised Problemmentioning

confidence: 99%

Preparation and Electrical Properties of Conducting Polyaniline-Polycarbonate Composite Films

Yin

Yoshino

Hashizume

et al. 1997

Jpn. J. Appl. Phys.

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The Newton-Kantorovich computational method is applied to the inverse problem of reconstructing a conductivity from given boundary measurements. This paper provides the theoretical analysis necessary to provide rigorous derivations of the Frechet differential. Linearisations of the non-linear problem are examined and a numerical procedure for reconstructing general conductivities suggested. This procedure is illustrated by reconstructing one-dimensional conductivities.

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“…Other authors have considered the linear versions of several inverse problems involving the wave equation [30,31]. They use the well known Born approximation to linearise their problems.…”

Section: The Linearised Problemmentioning

confidence: 99%

Preparation and Electrical Properties of Conducting Polyaniline-Polycarbonate Composite Films

Yin

Yoshino

Hashizume

et al. 1997

Jpn. J. Appl. Phys.

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“…Extensive numerical solutions of the direct problem has been made by use of the Born approximation in both the electrical engineering and optical literature. In two dimensions [16] and three dimensions [13] use has been made of this approach to solve the inverse scattering problem.…”

Section: 2mentioning

confidence: 99%

On Frechet differentiability of some nonlinear operators occurring in inverse problems: an implicit function theorem approach

Connolly¹,

Wall²

1990

Inverse Problems

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The validity of Newton-Kantorovich methods for the computational solution of inverse problems is directly linked to the Frechet differentiability of the appropriate non-linear operator. This paper illustrates how use of the implicit function theorem can considerably simplify the analysis of Frechet differentiability and regularity properties of this underlying operator. Two widely studied boundary and exterior measurement inverse problems are considered and new regularity results are produced.Physics Classification numbers: 0260, 0270, 1000, 4320.

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“…The Born approximation has been used in twoand three-dimensional problems [Lam et al, 1976;Fedotowsky et al, 1971;Bertero et al, 1980] leading to Fourier transform equations as in (16). Monostatic and multistatic measurements have been used.…”

Section: Low-frequency Approximationmentioning

confidence: 99%