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269
Calderón’s inverse problem for anisotropic conductivity
 in the plane, Comm. Partial Differential Equations 30
, 2005
"... Abstract: We study inverse conductivity problem for an anisotropic conductivity σ ∈ L ∞ in bounded and unbounded domains. Also, we give applications of the results in the case when DirichlettoNeumann and NeumanntoDirichlet maps are given only on a part of the boundary. 1. ..."
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Cited by 49 (14 self)
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Abstract: We study inverse conductivity problem for an anisotropic conductivity σ ∈ L ∞ in bounded and unbounded domains. Also, we give applications of the results in the case when DirichlettoNeumann and NeumanntoDirichlet maps are given only on a part of the boundary. 1.
Multiscale scientific computation: Review 2001
 Multiscale and Multiresolution Methods
, 2001
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Uniqueness in the Inverse Conductivity Problem for Conductivites with 3/2 Derivatives in L^p, p > 2n
"... this paper, we contribute nothing to the analysis of G # . The estimates used are from the paper of Sylvester and Uhlmannn [16]. It is possible that some improvement can be made here. We expect that one should be able to prove uniqueness for conductivities which have 3/2 derivatives in L with p & ..."
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Cited by 44 (0 self)
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this paper, we contribute nothing to the analysis of G # . The estimates used are from the paper of Sylvester and Uhlmannn [16]. It is possible that some improvement can be made here. We expect that one should be able to prove uniqueness for conductivities which have 3/2 derivatives in L with p > 2n/3. However, the straightforward generalization of the argument presented below would require that f # #G # f map functions which are compactly supported to functions which are locally in L with p and r satisfying 1/p 1/r = 1/n. Many such estimates fail, see [2] for further discussion
2007 On uniqueness in the inverse conductivity problem with local data Inverse Probl
 Imaging
"... The inverse condictivity problem with many boundary measurements consists of recovery of conductivity coefficient a (principal part) of an elliptic equation in a domain Ω ⊂ Rn, n = 2, 3 from the Neumann data given for all Dirichlet data (DirichlettoNeumann map). Calderon [5] proposed the ..."
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Cited by 42 (0 self)
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The inverse condictivity problem with many boundary measurements consists of recovery of conductivity coefficient a (principal part) of an elliptic equation in a domain Ω ⊂ Rn, n = 2, 3 from the Neumann data given for all Dirichlet data (DirichlettoNeumann map). Calderon [5] proposed the
A global stability estimate for the Gel’fandCalderón inverse problem in two dimensions
, 2010
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Electric Field Imaging
, 1999
"... The physical user interface is an increasingly significant factor limiting the effectiveness of our interactions with and through technology. This thesis introduces Electric Field Imaging, a new physical channel and inference framework for machine perception of human action. Though electric field se ..."
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Cited by 36 (5 self)
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The physical user interface is an increasingly significant factor limiting the effectiveness of our interactions with and through technology. This thesis introduces Electric Field Imaging, a new physical channel and inference framework for machine perception of human action. Though electric field sensing is an important sensory modality for several species of fish, it has not been seriously explored as a channel for machine perception. Technological applications of field sensing, from the Theremin to the capacitive elevator button, have been limited to simple proximity detection tasks. This thesis presents a solution to the inverse problem of inferring geometrical information about the configuration and motion of the human body from electric field measurements. It also presents simple, inexpensive hardware and signal processing techniques for making the field measurements, and several new applications of electric field sensing. The signal
An implementation of the reconstruction algorithm of A Nachman for the 2D inverse conductivity problem. Inverse Problems
, 2000
"... Abstract. The 2D inverse conductivity problem requires one to determine the unknown electrical conductivity distribution inside a bounded domain ⊂ R2 from knowledge of the DirichlettoNeumann map. The problem has geophysical, industrial, and medical imaging (electrical impedance tomography) appli ..."
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Cited by 34 (8 self)
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Abstract. The 2D inverse conductivity problem requires one to determine the unknown electrical conductivity distribution inside a bounded domain ⊂ R2 from knowledge of the DirichlettoNeumann map. The problem has geophysical, industrial, and medical imaging (electrical impedance tomography) applications. In 1996 A Nachman proved that the DirichlettoNeumann map uniquely determines C2 conductivities. The proof, which is constructive, outlines a direct method for reconstructing the conductivity. In this paper we present an implementation of the algorithm in Nachman’s proof. The paper includes numerical results obtained by applying the general algorithms described to two radially symmetric cases of small and large contrast. (Some figures in this article are in colour only in the electronic version; see www.iop.org) 1.
Invisibility and Inverse Problems
, 2008
"... We describe recent theoretical and experimental progress on making objects invisible. Ideas for devices that would have once seemed fanciful may now be at least approximately realized physically, using a new class of artificially structured materials, metamaterials. The equations that govern a var ..."
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Cited by 32 (19 self)
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We describe recent theoretical and experimental progress on making objects invisible. Ideas for devices that would have once seemed fanciful may now be at least approximately realized physically, using a new class of artificially structured materials, metamaterials. The equations that govern a variety of wave phenomena, including electrostatics, electromagnetism, acoustics and quantum mechanics, have transformation laws under changes of variables which allow one to design material parameters that steer waves around a hidden region, returning them to their original path on the far side. Not only are observers unaware of the contents of the hidden region, they are not even aware that something is being hidden; the object, which casts no shadow, is said to be cloaked. Proposals for, and even experimental implementations of, such cloaking devices have received the most attention, but other devices having striking effects on wave propagation, unseen in nature, are also possible. These designs are initially based on the transformation laws of the relevant PDEs, but due to the singular transformations needed for the desired effects, care needs to be taken in formulating and analyzing physically meaningful solutions. We recount the recent history of the subject and discuss some of the mathematical and physical issues involved.
Formulae and equations for finding scattering data from the DirichlettoNeumann map with nonzero background potential
 Inverse Problems
"... For the Schrödinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the DirichlettoNeumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Nov ..."
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Cited by 31 (12 self)
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For the Schrödinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the DirichlettoNeumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation −∆ψ + (v(x) − Eu(x))ψ = 0, Funkt. Anal. i Ego Prilozhen