A Reduced Order Model Approach to Inverse Scattering in Lossy Layered Media

Borcea, Liliana; Druskin, Vladimir; Zimmerling, Jörn

doi:10.1007/s10915-021-01616-7

Cited by 14 publications

(9 citation statements)

References 27 publications

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“…We refer to this step as embedding of the ROM in physical space and it is this embedding procedure that allows us to determine the medium parameters on the spatial interval of interest. Applications of the inverse problems considered in this paper can be found in radar, geophysical exploration in crystalline bedrock, ground penetrating radar, and any other field where one-dimensional imaging is relevant [4]. The characterisation of transmission lines (wave speed reconstruction along coax cables, printed circuit boards, etc) also belongs to this problem class [5,11].…”

Section: Introductionmentioning

confidence: 99%

“…We consider the recovery of a velocity profile from the first poles and residues of the impedance function, the so-called truncated spectral measure. An implementation of this procedure in terms of travel time coordinates is presented in [4]. Here, we take this optimal grid procedure as a starting point and present optimal grid embedding in terms of spatial coordinates instead of travel time coordinates.…”

Section: Introductionmentioning

confidence: 99%

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Solving inverse scattering problems via reduced-order model embedding procedures

Zimmerling,

Druskin,

Guddati

et al. 2023

Inverse Problems

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We present a reduced-order model (ROM) methodology for inverse scattering problems in which the ROMs are data-driven, i.e. they are constructed directly from data gathered by sensors. Moreover, the entries of the ROM contain localised information about the coefficients of the wave equation. We solve the inverse problem by embedding the ROM in physical space. Such an approach is also followed in the theory of ‘optimal grids,’ where the ROMs are interpreted as two-point finite-difference discretisations of an underlying set of equations of a first-order continuous system on this special grid. Here, we extend this line of work to wave equations and introduce a new embedding technique, which we call Krein embedding, since it is inspired by Krein’s seminal work on vibrations of a string. In this embedding approach, an adaptive grid and a set of medium parameters can be directly extracted from a ROM and we show that several limitations of optimal grid embeddings can be avoided. Furthermore, we show how Krein embedding is connected to classical optimal grid embedding and that convergence results for optimal grids can be extended to this novel embedding approach. Finally, we also briefly discuss Krein embedding for open domains, that is, semi-infinite domains that extend to infinity in one direction.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solving inverse scattering problems via reduced-order model embedding procedures

Zimmerling,

Druskin,

Guddati

et al. 2023

Inverse Problems

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“…The aerodynamic lift, drag and velocity distributions of the variant aircraft in the two sweep modes were analyzed and discussed 22 . When there were geometrically complex scattering obstacles, ray tracing became expensive or difficult to handle 23 , 24 . The measurement algorithm of the wing folding angle based on the three-axis accelerometer was designed, and the attitude of the fuselage and the wing relative to the reference coordinate system was accurately calculated 25 .…”

Section: Introductionmentioning

confidence: 99%

Z-folding aircraft electromagnetic scattering analysis based on hybrid grid matrix transformation

Zhou

Huang

2022

Sci Rep

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To study the electromagnetic scattering characteristics of a morphing aircraft with Z-folding wings, a method of hybrid grid matrix transformation (HGMT) is presented. The radar cross-section (RCS) of the aircraft in the four Z-folding modes is calculated and analyzed. When considering the deflection of the outer wing separately, the RCS of the wing under the head and side azimuth shows obvious dynamic characteristics, while the peak and fluctuation range are quite different. When the mid wing and the outer wing are deflected upwards together, the RCS of the aircraft under the positive side direction could be significantly reduced. When the mid wing deflects upward and the outer wing remains level, the peak of the side RCS of the aircraft is slightly reduced. When the mid wing deflects upwards and the outer wing deflects downwards, this peak indicator is further reduced, while the local fluctuation of the side RCS of the aircraft is increased. The HGMT method is effective to study the electromagnetic scattering characteristics of the Z-folding aircraft.

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“…In the ROM framework for solving multidimensional inverse problems, the ROM is constructed from a symmetric data set, that is, for coinciding source and receiver pairs. That is, the ROM is chosen precisely to match this data set, see [13,11,7,8,5,10,9]. Then, the ROM is transformed to a sparse form (tridiagonal for single input single output (SISO) problems, block tridiagonal for multiple input/output (MIMO) problems) by Lanczos orthogonalization.…”

Section: Introductionmentioning

confidence: 99%

On extension of the data driven ROM inverse scattering framework to partially nonreciprocal arrays

Druskin,

Moskow,

Zaslavsky

2021

Preprint

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Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated transmitters and receivers, that is, square symmetric matrix (data) transfer functions. To relax this limitation, we use our previous work [14], where the ROMs were combined with the Lippmann-Schwinger integral equation to produce a direct nonlinear inversion method. In this work we extend this approach to more general transfer functions, including those that are non-symmetric, e.g., obtained by adding only receivers or sources. The ROM is constructed based on the symmetric subset of the data and is used to construct all internal solutions. Remaining receivers are then used directly in the Lippmann-Schwinger equation. We demonstrate the new approach on a number of 1D and 2D examples with non-reciprocal arrays, including a single input/multiple outputs (SIMO) inverse problem, where the data is given by just a single-row matrix transfer function.

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A Reduced Order Model Approach to Inverse Scattering in Lossy Layered Media

Cited by 14 publications

References 27 publications

Solving inverse scattering problems via reduced-order model embedding procedures

Solving inverse scattering problems via reduced-order model embedding procedures

Z-folding aircraft electromagnetic scattering analysis based on hybrid grid matrix transformation

On extension of the data driven ROM inverse scattering framework to partially nonreciprocal arrays

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