Analysis of subspace migrations in limited-view inverse scattering problems

Applied Mathematics Letters

2018

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Various studies have confirmed the possibility of identifying the location of a set of small inhomogeneities via a direct sampling method; however, when their permeability differs from that of the background, their location cannot be satisfactorily identified. However, no theoretical explanation for this phenomenon has been verified. In this study, we demonstrate that the indicator function of the direct sampling method can be expressed by the Bessel function of order one of the first kind and explain why the exact locations of inhomogeneities cannot be identified. Numerical results with noisy data are exhibited to support our examination.

Section: Introductionmentioning

confidence: 99%

Detection of small inhomogeneities via direct sampling method in transverse electric polarization

Applied Mathematics Letters

2018

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“…Our current research considers cracks with Dirichlet boundary conditions; we plan to extend our research to cracks with Neumann boundary conditions (soundhard arc in inverse acoustic scattering problem), refer to [11,12]. Furthermore, motivated by [2,7,10,18,20], extending our research to the limited-view inverse scattering problem will be an interesting research topic. …”

Section: Results Of Numerical Simulations and Finding Exact Locationsmentioning

confidence: 99%

Appearance of inaccurate results in the MUSIC algorithm with inappropriate wavenumber

Journal of Inverse and Ill-Posed Problems

2017

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Abstract. MUltiple SIgnal Classification (MUSIC) is a well-known non-iterative location detection algorithm for small, perfectly conducting cracks in inverse scattering problems. However, when the applied wavenumbers are unknown, inaccurate locations of targets are extracted by MUSIC with inappropriate wavenumbers, a fact that has been confirmed by numerical simulations. To date, the reason behind this phenomenon has not been theoretically investigated. Motivated by this fact, we identify the structure of MUSIC-type imaging functionals with inappropriate wavenumbers by establishing a relationship with Bessel functions of order zero of the first kind. This result explains the reasons for inaccurate results. Various results of numerical simulations with noisy data support the identified structure of MUSIC.

“…Based on recent works [3,10,11,15,20], multi-frequency based imaging function yields better results than single-frequency based one. In contrast, in the limited-view problem, one cannot obtain a good result via multi-frequency MUSIC algorithm, refer to [16].…”

Section: Structure Of Music-type Imaging Function In Limited-view Promentioning

confidence: 99%

Properties of Music-Type Algorithm for Imaging of Thin Dielectric Inhomogeneity in Limited-View Inverse Scattering Problem

2014

PIER M

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Abstract-It is well known that a Multiple Signal Classification (MUSIC)-type algorithm yields good results in the imaging of thin dielectric inhomogeneity for full-view inverse scattering problems. In contrast, it yields a poor result in limited-view inverse scattering problems. In this paper, we verify the reason for the above by establishing a relationship between a MUSIC-type imaging function and the Bessel functions of the integer order of the first kind. This verification is based on the asymptotic expansion formula for thin dielectric inhomogeneity. Various numerical examples are discussed for confirming our verification.