An inverse problem for the three dimensional vector helmholtz equation for a perfectly conducting obstacle

Maponi, Pierluigi; Misici, Luciano; Zirilli, Francesco

doi:10.1016/0898-1221(91)90139-u

Cited by 19 publications

(6 citation statements)

References 6 publications

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“…LSM is a very rapid computational method when compared with other optimization approaches, as it requires very few priori data and involves only the solutions of linear ill-posed problems. Detecting unknown objects using LSM has found diverse applications in many areas, such as target identification, ground penetrating radars (GPR), medical diagnostics for cancer, and hypothermia [16,17].…”

Section: Introductionmentioning

confidence: 99%

Frequency and Polarization-Diversified Linear Sampling Methods for Microwave Tomography and Remote Sensing Using Electromagnetic Metamaterials

et al. 2017

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Metamaterial leaky wave antennas (MTM-LWAs), one kind of frequency scanning antennas, exhibit frequency-space mapping characteristics that can be utilized to obtain a sufficient field of view (FOV) and reconstruct shapes in both remote sensing and microwave imaging. In this article, we utilize MTM-LWAs to conduct a spectrally encoded three-dimensional (3D) microwave tomography and remote sensing that can reconstruct conductive targets with various dimensions. In this novel imaging technique, we employ the linear sampling method (LSM) as a powerful and fast reconstruction approach. Unlike the traditional LSM using only one single frequency to illuminate a fixed direction, the proposed method utilizes a frequency scanning MTM antenna array able to accomplish frequency-space mapping over the targeted 3D background that includes unknown objects. In addition, a novel technique based on a frequency and polarization hybrid method is proposed to improve the shape reconstruction resolution and stability in ill-posed inverse problems. Both simulation and experimental results demonstrate the unique advantages of the proposed LSM using MTM-LWAs with frequency and polarization diversity as an efficient 3D remote sensing and tomography scheme.

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Section: Introductionmentioning

confidence: 99%

Frequency and Polarization-Diversified Linear Sampling Methods for Microwave Tomography and Remote Sensing Using Electromagnetic Metamaterials

et al. 2017

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“…In this paper we introduce a numerical method to solve this inverse problem based on the Herglotz wave function method introduced by Colton and Monk in [11 and further developed by Misici, Zirilli, and their coauthors in [12]- [15]. In particular, based on previous work by Misici and Zirilli 14], we extend the Herglotz function method introduced in 11 for acoustically soft obstacles to hard obstacles or obstacles characterized by an acoustic impedance.…”

Section: Onmentioning

confidence: 97%

Three-Dimensional Inverse Obstacle Scattering for Time Harmonic Acoustic Waves: A Numerical Method

Misici¹,

Zirilli²

1994

SIAM J. Sci. Comput.

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“…Furthermore, we note that the convergence to the true obstacle failed when the single-frequency scheme was used with a higher frequency (k = 2.0). It is also noteworthy that when, instead of using the amplitude-based misfit functional, we used J 1 [defined in (14)], convergence to the true scatterer failed for the same initial guess and overall configuration; convergence was possible only when the initial guess came very close to the target. Thus far, these results lend support to the claim that the combination of the amplitude-based misfit functional with the frequencycontinuation scheme alleviate the difficulties associated with the solution multiplicity.…”

Section: Example I: Circular Scatterermentioning

confidence: 99%

“…One may roughly classify the approaches that have been followed, into methods that rely on optimization-based schemes (e.g. [1][2][3][4][11][12][13][14][15][16][17][18]), and methods that do not explicitly seek to minimize a misfit functional (e.g. [19][20][21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

Partial-differential-equation-constrained amplitude-based shape detection in inverse acoustic scattering

Kallivokas

2007

Comput Mech

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In this article we discuss a formal framework for casting the inverse problem of detecting the location and shape of an insonified scatterer embedded within a twodimensional homogeneous acoustic host, in terms of a partialdifferential-equation-constrained optimization approach. We seek to satisfy the ensuing Karush-Kuhn-Tucker first-order optimality conditions using boundary integral equations. The treatment of evolving boundary shapes, which arise naturally during the search for the true shape, resides on the use of total derivatives, borrowing from recent work by Bonnet and Guzina [1-4] in elastodynamics. We consider incomplete information collected at stations sparsely spaced at the assumed obstacle's backscattered region. To improve on the ability of the optimizer to arrive at the global optimum we: (a) favor an amplitude-based misfit functional; and (b) iterate over both the frequency-and wave-direction spaces through a sequence of problems. We report numerical results for soundhard objects with shapes ranging from circles, to penny-and kite-shaped, including obstacles with arbitrarily shaped nonconvex boundaries.

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An inverse problem for the three dimensional vector helmholtz equation for a perfectly conducting obstacle

Cited by 19 publications

References 6 publications

Frequency and Polarization-Diversified Linear Sampling Methods for Microwave Tomography and Remote Sensing Using Electromagnetic Metamaterials

Frequency and Polarization-Diversified Linear Sampling Methods for Microwave Tomography and Remote Sensing Using Electromagnetic Metamaterials

Three-Dimensional Inverse Obstacle Scattering for Time Harmonic Acoustic Waves: A Numerical Method

Partial-differential-equation-constrained amplitude-based shape detection in inverse acoustic scattering

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