A modification of the factorization method for scatterers with different physical properties

Furuya, Takashi

doi:10.1002/mma.5630

Cited by 3 publications

(3 citation statements)

References 16 publications

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“…Remark 3.2. It has been well-known that in theorem 2.1 of [23] the assumption (c) can be replaced by the injectivity of T, and it has been mainly used especially for the relaxation of the assumption that the wave number k > 0 is not a transmission eigenvalue in inverse medium scatterings (see e.g., [7,19,20,23]). However, it was found that this replacement is not correct (see remark 3.2 of [8]), thus the factorization method for inverse medium scatterings essentially needs the assumption of transmission eigenvalues.…”

Section: The Factorization Methodsmentioning

confidence: 99%

Remarks on the factorization and monotonicity method for inverse acoustic scatterings

Furuya

2021

Inverse Problems

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We study the factorization and monotonicity method for inverse acoustic scattering problems. Firstly, we give a new general functional analysis theorem for the monotonicity method. Comparing with the factorization method, the general theorem of the monotonicity generates reconstruction schemes under weaker a priori assumptions for unknown targets, and can directly deal with mixed problems so that the unknown targets have several different boundary conditions. Using the general theorem, we give the reconstruction scheme for the mixed crack that the Dirichlet boundary condition is imposed on one side of the crack and the Neumann boundary condition on the other side, which is a new extension of the monotonicity method.

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Section: The Factorization Methodsmentioning

confidence: 99%

Remarks on the factorization and monotonicity method for inverse acoustic scatterings

Furuya

2021

Inverse Problems

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“…Remark 3.2. It has been well known that in Theorem 2.1 of [22] the assumption (c) can be replaced by the injectivity of T , and it has been mainly used especially for the relaxation of the assumption that the wave number k > 0 is not a transmission eigenvalue in inverse medium scatterings (see e.g., [7,18,19,22]). However, it was found that this replacement is not correct (see Remark 3.2 of [8]), thus the factorization method for inverse medium scatterings essentially needs the assumption of transmission eigenvalues.…”

Section: The Factorization Methodsmentioning

confidence: 99%

“…The factorization method has first been introduced by Kirsch ( [16]) for the inverse acoustic obstacle scattering. It has been studied so far by many authors (see e.g., [1,3,4,7,11,17,18,19,20,22,24]), and it is well known as one of classical qualitative methods, which includes the linear sampling method of Colton and Kirsch ([5]), the singular sources method of Potthast ([23]), the probe method of Ikehata ([15]), etc. The monotonicity method, on the other hand, has been recently introduced by Harrach in [14] for the electrical impedance tomography.…”

Section: Introductionmentioning

confidence: 99%

Remarks on the factorization and monotonicity method for inverse acoustic scatterings

Furuya

2021

Preprint

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We study the factorization and monotonicity method for inverse acoustic scattering problems. Firstly, we newly give the general functional analysis theorem for monotonicity method. Comparing with the factorization method, the general theorem of the monotonicity generates reconstruction schemes under weaker a priori assumptions for unknown targets, and directly can deal with mixed problems that unknown targets have several different boundary conditions. Using the general theorem, we give the reconstruction scheme for the mixed crack that the Dirichlet boundary condition is imposed on one side of the crack and the Neumann boundary condition on the other side, which would be a new extension of monotonicity method.

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The factorization and monotonicity method for the defect in an open periodic waveguide

Furuya

2020

Journal of Inverse and Ill-Posed Problems

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AbstractWe consider the inverse scattering problem to reconstruct the defect in an infinite medium with periodicity in the upper half space from near field data. This paper has two contributions. Firstly, we mention that there is a mistake in the factorization method of the earlier paper [A. Lechleiter, The factorization method is independent of transmission eigenvalues, Inverse Probl. Imaging 3 2009, 1, 123–138] and give the correct one. Secondly, we give two reconstruction algorithms for the unknown defect by a combination of the factorization method and the monotonicity method. We also give numerical examples based on the former algorithm.

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A modification of the factorization method for scatterers with different physical properties

Cited by 3 publications

References 16 publications

Remarks on the factorization and monotonicity method for inverse acoustic scatterings

Remarks on the factorization and monotonicity method for inverse acoustic scatterings

Remarks on the factorization and monotonicity method for inverse acoustic scatterings

The factorization and monotonicity method for the defect in an open periodic waveguide

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