Detection and classification from electromagnetic induction data

Ammari, Habib; Chen, Junqing; Chen, Zhiming; Volkov, Darko; Wang, Han

doi:10.1016/j.jcp.2015.08.027

Cited by 44 publications

(87 citation statements)

References 27 publications

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“…The extension of the analysis to nonsmooth boundaries will form part of our future work. However, numerical evidence from computing

\overset{ˇ}{\overset{ˇ}{M}}

for objects with edges indicates that our results are also likely to hold for such objects …”

Section: Complete Asymptotic Expansion Of (Hα−h0)(x) As α →mentioning

confidence: 99%

“…Remark To be able to characterise an unknown conducting permeable object from measurements of ( H α − H 0 )( x ), using Theorem , a range of alternative approaches are possible, which include adapting the algorithms described by Ammari and Kang for the EIT problem or using a statistical classifier . In the latter case, we assume that we have a set of possible candidate objects and we follow Ammari and Kang, to put these in canonical form such that the description B α = α B + z , for each object, implies that the origin for ξ coincides with the object's centre of mass and that the determinant of the Póyla‐Szegö tensor associated with B (ie,

scriptT false(μ_{r} false) false[B false]

for μ r ≠1 and

scriptT false(0 false) false[B false]

for μ r =1) is equal to 1 .…”

Section: Complete Asymptotic Expansion Of (Hα−h0)(x) As α →mentioning

confidence: 99%

“…Proof Building on the previous results in proposition 4.3 in Ammari et al and theorem 3.1 in Ledger and Lionheart, we set

{bold-italicF}_{scriptJ false(B false), e_{j}, J false(p false)}

to be the solution of

\begin{matrix} \nabla_{ξ} \times μ_{*}^{- 1} \nabla_{ξ} \times F_{scriptJ false(B false), e_{j}, J false(p false)} - normali ω σ_{*} α^{2} F_{scriptJ false(B false), e_{j}, J false(p false)} & = normali ω σ_{*} α^{2} {false(normalΠ false(bold-italicξ false) false)}_{J false(p false)} e_{j} \times bold-italicξ in scriptJ false(B false), \\ \nabla_{ξ} \cdot F_{scriptJ false(B false), e_{j}, J false(p false)} & = 0 in R^{3} \ scriptJ false(B false), \\ \nabla_{ξ} \times μ_{0}^{- 1} \nabla_{ξ} \times F_{scriptJ false(B false), e_{j}, J false(p false)} & = bold0 in R^{3} \ scriptJ false(B false), \\ false[bold-italicn \times \end{matrix}

…”

Section: Tensor Representationsmentioning

confidence: 99%

See 2 more Smart Citations

Generalised magnetic polarizability tensors

Ledger

Lionheart

2018

Math Methods in App Sciences

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We present a new complete asymptotic expansion for the low-frequency time-harmonic magnetic field perturbation caused by the presence of a conducting (permeable) object as its size tends to zero for the eddy current regime of Maxwell's equations. The new asymptotic expansion allows the characterisation of the shape and material properties of such objects by a new class of generalised magnetic polarizability tensors, and we provide an explicit formula for their calculation. Our result will have important implications for metal detectors since it will improve small object discrimination, and for situations where the background field varies over the inclusion, this information will be useable, and indeed useful, in identifying their shape and material properties. Thus, improving the ability of metal detectors to locate landmines and unexploded ordnance, sort metals in recycling processes, and ensure food safety as well as enhancing security screening at airports and public events.

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“…The extension of the analysis to nonsmooth boundaries will form part of our future work. However, numerical evidence from computing

\overset{ˇ}{\overset{ˇ}{M}}

for objects with edges indicates that our results are also likely to hold for such objects …”

Section: Complete Asymptotic Expansion Of (Hα−h0)(x) As α →mentioning

confidence: 99%

scriptT false(μ_{r} false) false[B false]

for μ r ≠1 and

scriptT false(0 false) false[B false]

for μ r =1) is equal to 1 .…”

Section: Complete Asymptotic Expansion Of (Hα−h0)(x) As α →mentioning

confidence: 99%

“…Proof Building on the previous results in proposition 4.3 in Ammari et al and theorem 3.1 in Ledger and Lionheart, we set

{bold-italicF}_{scriptJ false(B false), e_{j}, J false(p false)}

to be the solution of

\begin{matrix} \nabla_{ξ} \times μ_{*}^{- 1} \nabla_{ξ} \times F_{scriptJ false(B false), e_{j}, J false(p false)} - normali ω σ_{*} α^{2} F_{scriptJ false(B false), e_{j}, J false(p false)} & = normali ω σ_{*} α^{2} {false(normalΠ false(bold-italicξ false) false)}_{J false(p false)} e_{j} \times bold-italicξ in scriptJ false(B false), \\ \nabla_{ξ} \cdot F_{scriptJ false(B false), e_{j}, J false(p false)} & = 0 in R^{3} \ scriptJ false(B false), \\ \nabla_{ξ} \times μ_{0}^{- 1} \nabla_{ξ} \times F_{scriptJ false(B false), e_{j}, J false(p false)} & = bold0 in R^{3} \ scriptJ false(B false), \\ false[bold-italicn \times \end{matrix}

…”

Section: Tensor Representationsmentioning

confidence: 99%

See 1 more Smart Citation

Generalised magnetic polarizability tensors

Ledger

Lionheart

2018

Math Methods in App Sciences

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show abstract

“…The introduction of a known admissible class A in our algorithm is related to the dictionary matching algorithms that have been recently investigated in a series of works by Ammari and his collaborators [2,3,13], where some a priori known base shapes form a dictionary for the reconstruction. We also note that comparable indicator functions are used in a recent work [15] for reconstructing the acoustic scatterers at small scale and regular scale, respectively.…”

Section: Scheme IImentioning

confidence: 99%

Locating Multiple Multiscale Acoustic Scatterers

Li¹,

Liu²,

Zou³

2014

Multiscale Model. Simul.

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We develop three inverse scattering schemes for locating multiple multiscale acoustic scatterers in a very general and practical setting. For all of the three locating schemes, only one single far-field measurement is used. The number of the multiple scatterer components may be unknown, and each scatterer component is allowed to be an inhomogeneous medium with an unknown content or an impenetrable obstacle of sound-soft, sound-hard, or impedance type. Moreover, the scatterers could be multiscale; i.e., some scatterers may be of regular size, and some others may be of small size in terms of the wavelength of the detecting acoustic wave. If a scatterer component is of regular size, it is required that its shape (not necessarily its orientation, size, and location) should be from an admissible class which is known in advance. The locating schemes are based on some novel indicator functions and are computationally cheap and robust against the measurement noise. Rigorous mathematical justifications are provided for each scheme, and numerical experiments are presented to demonstrate its robustness and effectiveness.

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“…In applied mathematics and analysis, previous studies by [1,14,15,16,17,18,19] have shown that the perturbation due to the presence of the conducting objects can be represented by asymptotic formulas and PT is actually the dominant term in the formula. The asymptotic formula and the corresponding PT are generally not the same for different systems.…”

Section: Introductionmentioning

confidence: 99%

Classification of materials for conducting spheroids based on the first order polarization tensor

Khairuddin

Yunos

Aziz

et al. 2017

J. Phys.: Conf. Ser.

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Abstract. Polarization tensor is an old terminology in mathematics and physics with many recent industrial applications including medical imaging, nondestructive testing and metal detection. In these applications, it is theoretically formulated based on the mathematical modelling either in electrics, electromagnetics or both. Generally, polarization tensor represents the perturbation in the electric or electromagnetic fields due to the presence of conducting objects and hence, it also desribes the objects. Understanding the properties of the polarization tensor is necessary and important in order to apply it. Therefore, in this study, when the conducting object is a spheroid, we show that the polarization tensor is positive-definite if and only if the conductivity of the object is greater than one. In contrast, we also prove that the polarization tensor is negative-definite if and only if the conductivity of the object is between zero and one. These features categorize the conductivity of the spheroid based on in its polarization tensor and can then help to classify the material of the spheroid.

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Detection and classification from electromagnetic induction data

Cited by 44 publications

References 27 publications

Generalised magnetic polarizability tensors

Generalised magnetic polarizability tensors

Locating Multiple Multiscale Acoustic Scatterers

Classification of materials for conducting spheroids based on the first order polarization tensor

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