Inverse Acoustic Obstacle Scattering

Colton, David; Kreß, Rainer

doi:10.1007/978-1-4614-4942-3_5

Cited by 14 publications

(15 citation statements)

References 264 publications

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“…To numerically solve the inverse scattering problem described in the previous section, (2) and (3) should be discretized. To this end, support S is divided into N square cells with dimension Δd.…”

Section: Discretizationmentioning

confidence: 99%

“…The discretized inverse problem also suffers from ill-conditioning like its continuous counterpart as described in Section 2.1. The effects of ill-conditioning can be alleviated by constraining the minimization problem with a penalty term as [2,3]:…”

Section: Nonlinear Sparse Optimizationmentioning

confidence: 99%

“…Electromagnetic inverse scattering problem is defined as finding unknown material properties, such as dielectric permittivity or conductivity or both, in an investigation domain from scattered fields measured away from the domain itself [1][2][3]. Numerical methods for solving the inverse scattering problem are called for in various applications in engineering including but not limited to through-wall and tomography imaging [4][5][6], non-destructive testing [7], crack/mine detection [8,9], hydrocarbon reservoir exploration and monitoring [10,11], and radar and remote sensing [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…(ii) Ill-posedness: Integral operators used for expressing the scattered fields in terms of the permittivity have a "smoothening" effect. Smoothening combined with the facts that the number of measurements is finite and the measurements are noisy makes the inverse scattering problem ill-posed [1][2][3]5].…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, convolution integrals between τ (r )E u (r ) and G(r, r ) in (2) and (3) have a "smoothening" effect on the fast varying components of τ (r ) and E u (r ), which results in loss of information especially if E mea u (r R m ) are obtained from "noisy" measurements. These two factors make the inverse problem ill posed [1][2][3]. Furthermore, a closer look at (2) and (3) reveals that E sca u (r R m ) are nonlinear functions of τ (r) meaning that the inverse problem is nonlinear in τ (r).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Sparse Electromagnetic Imaging Using Nonlinear Landweber Iterations

Desmal¹,

Bağcı²

2015

PIER

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Abstract-A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L 0 /L 1 -norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L 0 /L 1 -norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the "measured" fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.

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Section: Discretizationmentioning

confidence: 99%

Section: Nonlinear Sparse Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sparse Electromagnetic Imaging Using Nonlinear Landweber Iterations

Desmal¹,

Bağcı²

2015

PIER

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A Generative Deep Learning Approach for Shape Recognition of Arbitrary Objects from Phaseless Acoustic Scattering Data

Ahmed

Farhat

Chen

et al. 2023

Advanced Intelligent Systems

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A generative deep learning approach for shape recognition of an arbitrary object from its acoustic scattering properties is proposed and demonstrated. The strategy exploits deep neural networks to learn the mapping between the latent space of a 2D acoustic object and the far‐field scattering amplitudes. A neural network is designed as an adversarial autoencoder and trained via unsupervised learning to determine the latent space of the acoustic object. Important structural features of the object are embedded in lower‐dimensional latent space which supports the modeling of a shape generator and accelerates the learning in the inverse design process. The proposed inverse design uses the variational inference approach with encoder‐ and decoder‐like architecture where the decoder is composed of two pretrained neural networks: the generator and the forward model. The data‐driven framework finds an accurate solution to the ill‐posed inverse scattering problem, where nonunique solution space is overcome by the multifrequency phaseless far‐field patterns. This inverse method is a powerful design tool that doesn't require complex analytical calculation and opens up new avenues for practical realization, automatic recognition of arbitrary‐shaped submarines or large fish, and other underwater applications.

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T‐Hex: Tilted hexagonal grids for rapid 3D imaging

Engel

Kasper

Wilm

et al. 2020

Magnetic Resonance in Med

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The purpose of this work is to devise and demonstrate an encoding strategy for 3D MRI that reconciles high speed with flexible segmentation, uniform k-space density, and benign T * 2 effects. Methods: Fast sampling of a 3D k-space is typically accomplished by 2D readouts per shot using EPI trains or spiral readouts. Tilted hexagonal (T-Hex) sampling is a way of acquiring more k-space volume per excitation while maintaining uniform sampling density and a smooth T * 2 filter. The k-space volume covered per shot is controlled by the tilting angle. Image reconstruction is performed with a 3D extension of the iterative SENSE approach, incorporating actual field dynamics and static off-resonance. T-Hex imaging is compared with established 3D schemes in terms of speed and noise performance. Results: Tilted hexagonal acquisition is found to achieve greater imaging speed than known alternatives, particularly in combination with spiral trajectories. The interplay of the proposed 3D trajectories, array detection, and off-resonance is successfully addressed by iterative inversion of the full signal model. Enhanced coverage per shot is of greatest utility for high speed in an intermediate resolution regime of 1 to 4 mm. T-Hex EPI combines the benefits of extended coverage per shot with increased robustness against off-resonance effects. Conclusion: Sampling of tilted hexagonal grids is a feasible means of gaining 3D imaging speed with near-optimal SNR efficiency and benign depiction properties. It is a particularly promising technique for time-resolved applications such as fMRI. K E Y W O R D S 3D encoding, algebraic image reconstruction, magnetic field monitoring, spiral imaging F I G U R E 1 Examples of 3D readout strategies: Concentric shells, yarnball, and interleaved multiplanar spirals. Black dots indicate that interleaves were omitted for better visibility | 2509 ENGEL Et aL.

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Inverse Acoustic Obstacle Scattering

Cited by 14 publications

References 264 publications

Sparse Electromagnetic Imaging Using Nonlinear Landweber Iterations

Sparse Electromagnetic Imaging Using Nonlinear Landweber Iterations

A Generative Deep Learning Approach for Shape Recognition of Arbitrary Objects from Phaseless Acoustic Scattering Data

T‐Hex: Tilted hexagonal grids for rapid 3D imaging

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