Imaging and Inverse Scattering in Nondestructive Evaluation with Acoustic and Elastic Waves

Langenberg, K. J.; Mayer, Klaus; Fellinger, P.; Marklein, R.

doi:10.1007/978-1-4615-2958-3_22

Cited by 7 publications

(10 citation statements)

References 3 publications

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“…If the target rotates in a known manner, then data collected as a function of time will also be data collected across an aperture. This is the idea behind inverse synthetic aperture imaging [3,[26][27][28][29][30][31][32][33][34]. Define coordinate directions î and ĵ, fixed at the radar, in terms of the rotation angle θ by î • R = − sin θ and ĵ • R = cos θ : the 'cross-range' and 'down-range' directions, respectively.…”

Section: The Inverse Synthetic Aperture Methodsmentioning

confidence: 99%

An observation about radar imaging of re-entrant structures with implications for automatic target recognition

Borden¹

1997

Inverse Problems

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The standard inverse synthetic aperture radar (ISAR) high-frequency weak-scatterer model is inappropriate to targets with inlets and cavities, and images created under this model assumption often display artifacts associated with these structures. Since inlets and cavities (typically) make a strong contribution to the radar field scattered from aircraft targets, these artifacts often confound the image interpretation process and considerable effort has been spent in recent years to model, isolate, and remove these sources of error. Many of the more complete and accurate scattering models require extensive knowledge about the cavity/inlet shape and size and, moreover, are numerically intensive-features that make them unsuitable for many imaging applications. We examine an older (and less accurate) model based on a weak-scattering modal expansion of the structure which appears to be well suited to ISAR imaging. In addition, the analysis shows how cavity/inlet shape-specific information may be estimated from an ordinary ISAR image.

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Section: The Inverse Synthetic Aperture Methodsmentioning

confidence: 99%

An observation about radar imaging of re-entrant structures with implications for automatic target recognition

Borden¹

1997

Inverse Problems

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“…It is apparent that the set of basis functions that span Ψ can be used to discretize the operators in (6). Using a Galerkin approach, we arrive at a system of equations ZI = V, where…”

Section: Properties Of Loop Subdivision Basismentioning

confidence: 99%

“…Research into inverse scattering dates back decades and has found applications in a number of wide ranging fields of studies, including areas such as medical diagnostics, detection of buried objects, tomography, and nondestructive evaluation [1,2,3,4,5,6]; in these problems, the goal is to retrieve the distribution of constitutive properties in a domain and/or geometry given a set of measured scattered field data. Along these lines of an inverse scattering problem, there are two subclasses of problems that can be considered: can one (a) modify shapes such that one obtains desired scattered fields, or (b) reconstruct the shape of a object given scattered field data (and boundary conditions on the surface).…”

Section: Introductionmentioning

confidence: 99%

Laplace-Beltrami based Multi-Resolution Shape Reconstruction on Subdivision Surfaces

Alsnayyan,

Shanker

2021

Preprint

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The eigenfunctions of the Laplace-Beltrami operator have widespread applications in a number of disciplines of engineering, computer vision/graphics, machine learning, etc. These eigenfunctions or manifold harmonics, provide the means to smoothly interpolate data on a manifold. They are highly effective, specifically as it relates to geometry representation and editing; manifold harmonics form a natural basis for multi-resolution representation (and editing) of complex surfaces and functioned defined therein. In this paper, we seek to develop the framework to exploit the benefits of manifold harmonics for shape reconstruction. To this end, we develop a highly compressible, multi-resolution shape reconstruction scheme using manifold harmonics. The method relies on subdivision basis sets to construct both boundary element isogeometric methods for analysis and surface finite elements to construct manifold harmonics. We pair this technique with volumetric source reconstruction method to determine an initial starting point. Examples presented highlight efficacy of the approach in the presence of noisy data, including significant reduction in the number of degrees of freedom for complex objects, accuracy of reconstruction, and multi-resolution capabilities.

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“…Inverse scattering finds applications in medical imaging [13,37,41,48,49,51,[53][54][55]59], remote sensing [38,60,61], ocean acoustics [22,25], nondestructive testing [14,26,30,42,45,46], geophysics [6,32,56,58,64], and sonar and radar [18,24,27]. In this work, we recover a compactly supported unknown scatterer, denoted q(x), in the presence of a compactly supported random background medium denoted by η(x), from the scattered field measurements.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of a compactly supported sound profile in the presence of a random background medium

Borges

Biros

2018

Inverse Problems

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In this paper, we present algorithms for reconstructing an unknown compact scatterer embedded in a random noisy background medium, given measurements of the scattered field and information about the background medium and the sound profile. We present six different methods for the solution of this inverse problem using different amounts of scattered data and prior information about the random background medium and the scatterer. The different inversion algorithms are defined by a combination of stochastic programming methods and Bayesian formulation. Our basic results show that if we have data for just one instance of the random background medium the best strategy is to invert for both random medium and unknown scatterer with appropriate regularization. However, if we have data for multiple instances of the medium it may be worth solving a coupled set of multiple inverse problems. We present several numerical results for inverting for various scatterer geometries under different inversion scenarios. The main take-away of our study is that one should invert for both unknown scatterer and random medium, with appropriate, prior-information based regularization. Furthermore, if data from multiple realizations of the background medium is available, then it may be beneficial to combine results from multiple inversions.

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Imaging and Inverse Scattering in Nondestructive Evaluation with Acoustic and Elastic Waves

Cited by 7 publications

References 3 publications

An observation about radar imaging of re-entrant structures with implications for automatic target recognition

An observation about radar imaging of re-entrant structures with implications for automatic target recognition

Laplace-Beltrami based Multi-Resolution Shape Reconstruction on Subdivision Surfaces

Reconstruction of a compactly supported sound profile in the presence of a random background medium

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