A direct impedance tomography algorithm for locating small inhomogeneities

We establish an asymptotic representation formula for the steady state current perturbations caused by internal corrosive boundary parts of small surface measure. Based on this formula we design a non-iterative method of MUSIC (multiple signal classification) type for localizing the corrosive parts from voltage-to-current observations. We perform numerical experiments to test the viability of the algorithm and the results clearly demonstrate that the algorithm works well even in the presence of relatively high noise ratios.Mathematics subject classification (MSC2000): 35R30

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“…Exactly as in Brühl et al [4] there is a simple factorization of the operator T , and a corresponding characterization of its range.…”

Section: Lemma 52mentioning

confidence: 90%

“…This algorithm is of MUSIC-type (multiple signal classification) and is based on an accurate asymptotic representation formula for the steady state boundary currents. In many ways it is closely related to the algorithm developed in [4] for the purpose of detection of small internal defects.…”

Section: Introductionmentioning

confidence: 99%

A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements

et al. 2007

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“…It may be useful to compare these measurement counts to those related to another method (a linear "linear sampling" method) which has recently been proposed as a tool for the reconstruction of collections of small inhomogeneities (see [6]). For the accurate reconstruction of the location of m inhomogeneities this method requires knowledge of the subspace spanned by the first 2m eigenvectors of the incremental Dirichlet to Neumann data operator.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…M (j) is given by 6) where, for 0 < c j = γ0 γj < ∞ and 1 ≤ l ≤ n, φ l (y) is the unique solution to…”

Section: Introductionmentioning

confidence: 99%

Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

2003

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Abstract. In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.Mathematics Subject Classification. 35J25, 35R30, 65R99.

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“…The asymptotic formulas for diametrically small conductivity inhomogeneities and scatterers known so far form the foundation of several efficient reconstruction methods for inverse conductivity problems (see, e.g., Ammari, Moskow, and Vogelius [7], Ammari and Seo [8] or Brühl, Hanke, and Vogelius [17]) and inverse scattering problems for Maxwell's equations (see, e.g., Ammari et al [2], Iakovleva et al [33], Volkov [42], or [28,29,31,32]). In addition the general formula for electrostatic potentials from [18] has recently been used to investigate inverse conductivity problems for wires and tubes (see Beretta et al [13] or [30]).…”

Section: Introductionmentioning

confidence: 99%

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Griesmaier

2011

ESAIM: M2AN

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Abstract.In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This smallness typically causes problems when solving direct scattering problems due to the need to discretize the objects and also when solving inverse scattering problems because small objects have very little effect on electromagnetic fields. In this paper we consider an asymptotic representation formula for scattered electromagnetic waves caused by low volume objects contained in some otherwise homogeneous threedimensional bounded domain, assuming only that the scatterers are measurable and well-separated from the boundary of the domain. The formula yields a very general asymptotic model for electromagnetic scattering due to low volume objects that can either be used to simulate the corresponding electromagnetic fields or as the foundation of efficient reconstruction methods for inverse scattering problems with low volume scatterers.

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A direct impedance tomography algorithm for locating small inhomogeneities

Cited by 123 publications

References 18 publications

A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements

A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements

Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

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